Free Printable probability theory

1.

An event whose occurrence is impossible, is called

a)

Sure event

b)

Uncertain event

c)

Null event

d)

None of these

2.

If the occurrence of one of them excludes the possibility of the occurrence of the other, then the event is called ...

a)

Mutually exclusive/ Disjoint

b)

Independent

c)

Mutually exhaustive

d)

Sure event

3.

Number of combinations of 4 items taking 2 at a time, $4C_2\ =$

a)

5

b)

6

c)

0

d)

4

4.

If two events, A and B are mutually exclusive, then P(AUB) =

a)

P(A) + P(B)

b)

P(A) + P(B) - P(A $\cap$ B)

c)

P(A) $\times$ P(B)

d)

P(A)- P(B)

5.

A card is selected from a deck of cards. What is the probability that the card is Black ?

a)

$\frac{1}{52}$

b)

$\frac{1}{13}$

c)

$\frac{1}{2}$

d)

$\frac{1}{4}$

6.

Three coins are tossed simultaneously . The sample space will contain ... sample points.

a)

1

b)

2

c)

4

d)

8

7.

Two Coins are tossed. Let X be the Random Variable indicating the number of Heads. X can take the values ...

a)

0,1

b)

0,1,2

c)

0,1,2,3

d)

0,1,2,3,4

8.

Two Dice are tossed. What is the probability of getting sum of the numbers on the dice is 3

a)

$\frac{1}{36}$

b)

$\frac{1}{18}$

c)

$\frac{3}{36}$

d)

$\frac{3}{18}$

9.

The probability P(A/B) is called ....

a)

Independent probability

b)

Disjoint Events

c)

Sure Probability

d)

Conditional Probability

10.

How many 2 digit numbers can be formed using the digits of the number 6789 if repetition of numbers are not allowed ( 66, 77, 88 & 99 not allowed)?

a)

16

b)

12

c)

6

d)

8

11.

How many 2 digit numbers can be formed using the digits of the number 6789 if repetition of numbers are allowed ( 66, 77, 88 & 99 are allowed)?

a)

16

b)

12

c)

6

d)

8

12.

$find\ P\left(A\cup B\right).\$ when P(A)=0.3, P(B)=0.4, A and B are Mutually exclusive events.

a)

$0.3$

b)

$0.4$

c)

$0.7$

d)

$0.58$

13.

$find\ P\left(A\cup B\right).\$ when P(A)=0.3, P(B)=0.4, A and B are indendent events.

a)

$0.3$

b)

$0.4$

c)

$0.7$

d)

$0.58$

14.

$P\left(A\cup B\right)=0.6$ , $P\left(A\right)=0.5$ , $P\left(B\right)=0.2$ $find\ P\left(A\cap B\right)$

a)

$0$

b)

$0.2$

c)

$0.1$

d)

$0.7$

15.

$P\left(Atleast\ \ \ One\ \right)=\ \frac{5}{6}$ find $P\left(\ No\ \ \ \ One\right).$

a)

$\frac{5}{6}$

b)

$\frac{1}{6}$

c)

$\frac{2}{3}$

d)

$\frac{6}{5}$

16.

$C-Student\ of\ Commerce\ Dept.$ $E-\ Students\ of\ Economics\ Dept.$ $B\ -Boys\ of\ Our\ college\$ Then $E\cap C=\ ?$

a)

$\phi$

b)

$E-C$

c)

$E\cup C$

d)

$E\subset C$

17.

$P\left(A\right)=\ \frac{favourable\ Cases}{Total\ Cases}$ , This definition of probability is called ...

a)

Axiomatic Definition

b)

Classical Definition

c)

Frequency Definition

d)

Subjective Definition

18.

What is the probability of having 53 Sundays in a leap year ?

a)

$\frac{1}{366}$

b)

$\frac{1}{53}$

c)

$\frac{1}{7}$

d)

$\frac{2}{7}$

19.

When a die is thrown, ...................is the probability of getting a 5

a)

$\frac{1}{6}$

b)

$\frac{5}{6}$

c)

$\frac{1}{2}$

d)

$\frac{4}{5}$

20.

Two events are said to be independent if

a)

There is no common point in between them

b)

Both the events have only one point

c)

Each outcome has equal chance of occurrence

d)

One does not affect the occurrence of the other

21.

Sample space for the event of tossing two coins is

a)

$S=\left\{1,2,3,4,5,6\right\}$

b)

$S=\left\{H,T\right\}$

c)

$S=\left\{HH,\ HT,\ TH,\ TT\right\}$

d)

S={HHH,HHT,HTH,HTT,THT,TTH,THH,TTT}

22.

$P\left(A\cap B\right)\le P\left(A\right)$

a)

$True$

b)

$False$

23.

in Some Cases, P(A) can take negative values

a)

$True$

b)

$False$

24.

$P\left(A\right)=1.25.\$ is this possible for an event A ?

a)

Yes, its Possible

b)

$No,\ P\left(A\right)\$ cannot take a value geater than one

25.

Here the events A, B are called...

a)

Sure Events

b)

Null Events

c)

Disjoint Events

d)

Mutual Events

26.

A die is numbered as 1,2,3,4,5,6 on the faces. When this die is thrown the sample space is S = {1,2,3,4,5,6}

a)

True

b)

False

27.

a)

a

b)

b

c)

c

d)

d

28.

a)

a

b)

b

c)

c

29.

The probability of drawing a spade from a pack of 52 cards is

a)

$\frac{1}{52}$

b)

$\frac{1}{3}$

c)

$\frac{1}{4}$

d)

$\frac{4}{13}$

30.

a)

(i) and (ii) are true

b)

(i) is true and (ii) is false

c)

(i) is false and (ii) is true

d)

(i) and (ii) are false

31.

Two coins are tossed simultaneously, the probability of getting a head and a tail is

a)

1/2

b)

1/6

c)

1/4

d)

1/3

32.

a)

a

b)

b

c)

c

d)

d

33.

a)

a

b)

b

c)

c

d)

d

34.

a)

a

b)

b

c)

c

35.

Pairwise independence of n events ⇒ independence of n events

a)

True

b)

False

36.

If F(x) is a distribution function of the random variable X and if a < b then P(a < X ≤ b) is

a)

P(a)

b)

P(b)

c)

F(b) - F(a)

d)

F(a) - F(b)

37.

If X is a continuous random variable, the probability of every set consisting of a single point is

a)

zero

b)

one

c)

infinity

38.

A random variable X is a discrete random variable if it takes at most ______________values.

a)

a countable number of values

b)

an infinite number of values

c)

a countable or infinite number of values

39.

Choose the correct option by reading the statements about Mathematical expectation

(i) E(c)=c is where is a constant

(ii) E(c X) = c E(X) where c is a constant

(ⅲ)E(X+Y) =E(X). E(Y) (ⅳ) E(XY)=E(X)+E(Y)

a)

All the four statements are true

b)

Only (iii) and (iv) are true

c)

Only (i) and (ii) are true

d)

All the four statements are false

40.

The concept of _____________arises when we deal with variables like heights, weights, temperature which can take any value between certain limits.

a)

discrete random variable

b)

continuous random variable

c)

experiment

d)

probability

41.

a)

True

b)

False

42.

Any subset A of a sample space S is called

a)

an event

b)

sample points

c)

experiment

d)

exhaustive

43.

If A and B are two events with P (A) = 0.4, P (B) = 0.3 and P (A∩B) = 0.2. Find P (A∪B)

a)

0.5

b)

0.8

c)

0.1

d)

0.2

44.

Two dice numbered as 1,2, ……,6 on their faces are thrown. Let A be the event that the sum of the numbers on the faces shown is odd and B be the event that at least one number is 1. Then P (A ∩ B)

a)

1/2

b)

1/6

c)

1/3

d)

1/4

45.

Two dice numbered as 1,2, ……,6 on their faces are thrown. Let A be the event that the sum of the numbers on the faces shown is odd and B be the event that at least one number is 1. Then P (AυB)

a)

23/36

b)

29/36

c)

5/6

d)

11/72

46.

A bag contains 30 pieces of candy. There are 15 grape, 7 cherry, 3 lemon, 5 strawberry. What is the probability of drawing a lemon?

a)

3

b)

1/10

c)

3/10

d)

30%

47.

P(not A) =
*Remember to simplify.*

a)

6/8

b)

3/4

c)

2/8

d)

1/4

48.

Rolling a 15 on a number cube is

a)

Impossible

b)

Certain

c)

Unlikely

d)

Equally Likely

49.

What is the probability the spinner stops on yellow?

a)

.075

b)

50%

c)

25%

d)

3/8

50.

A die is rolled. What is the probability that the result is less than 3 ?

a)

1/2

b)

1/3

c)

1/4

d)

1/6

51.

A box has 3 limes, 5 grapes, and 2 oranges.

P (not lime)

a)

3/10

b)

30%

c)

7/10

d)

Answer Not Here

52.

Marvin has a standard deck of cards.

(52 in a deck, 4 suits)

P (Ace or a 5)

a)

1/13

b)

2/13

c)

1/26

d)

8/50

53.

Amelia receives a treat bag. The treat bag contains 10 gumballs, 5 pixie sticks, 2 bracelets, and 3 chocolates. If Amelia selects 3 items from her treat bag without looking and gives them to her sister, which could NOT represent a possible outcome for the items Amelia selects?

a)

gumball, gumball, gumball

b)

pixie stick, gumball, chocolate

c)

bracelet, bracelet, bracelet

d)

gumball, gumball, pixie stick

54.

The list shows all possible outcomes for which experiment?

S = { (heads, heads), (heads, tails),

(tails, tails), (tails, heads) }

a)

Flipping a coin one time

b)

Flipping a coin two times

c)

Flipping a coin three times

d)

Flipping a coin four times

55.

A jar contains 2 pink, 6 red, and 4 blue marbles. If you pick one marble without looking, what is the probability that the marble you pick will be red or blue?

a)

5/6

b)

1/2

c)

1/3

d)

1/6

56.

What is the probability of choosing a vowel from the alphabet?

a)

21/26

b)

5/26

c)

1/21

d)

7/21

57.

Which of the following are possible samples spaces for tossing 2 coins? (May be more than one correct answer)

a)

{H, T, H, T}

b)

{HH, HT, TH, TT}

c)

{H, T}

d)

{T, H}

e)

{TT, HH, TH, HT}

58.

Which of the following shows or illustrates MUTUALLY EXCLUSIVE EVENTS?

a)

Getting a diamond card or spade card in a deck of cards

b)

Getting a face card or an ace in a deck of cards

c)

Getting an ace and a red card in a deck of cards

d)

Getting a heart or a face card

59.

Which of the following shows or illustrates INCLUSIVE EVENTS?

a)

Getting a diamond card or spade card in a deck of cards

b)

Getting a face card or an ace in a deck of cards

c)

Getting an ace and a red card in a deck of cards

d)

Getting a heart or a face card

60.

Which of the following shows or illustrates MUTUALLY EXCLUSIVE EVENTS?

a)

Getting an even number or an odd number in rolling a die

b)

Getting 4 or a number greater than 2 in rolling a die

c)

Getting 1 or a number less than 3 in rolling a die

d)

Getting a heart or a face card

61.

In a room with 28 people, there are 5 women wearing red and 7 wearing blue, and there are 6 men wearing red and 10 men wearing purple. What is the probability of randomly picking one person who is either wearing red or is a male?

a)

$\frac{11}{28}$

b)

$\frac{16}{28}$

c)

$\frac{3}{14}$

d)

$\frac{3}{4}$

62.

Find the probability of drawing an ace or a red card in a standard deck of 52 cards.

a)

$\frac{1}{13}$

b)

$\frac{1}{2}$

c)

$\frac{1}{26}$

d)

$\frac{7}{13}$

63.

What is the probability of tossing a coin four times and getting tails each time?

a)

1/16

b)

1/8

c)

1/2

d)

1/4

64.

A number cube is rolled and a coin is tossed. What is the probability of rolling a number greater than 4 and tossing tails?

a)

1/6

b)

1/3

c)

1/2

d)

1/4

65.

When randomly drawing from a standard deck of 52 playing cards, what is the probability of drawing a 9 four times in a row if the cards are not replaced?

a)

1/5,525

b)

1/270,725

c)

1/28,561

d)

1/4

66.

Given a standard deck of 52 playing cards, what is the probability of randomly drawing a 2 and then a 3 if the first card is not replaced?

a)

1/13

b)

4/663

c)

1/676

d)

1/169

67.

Two marbles are drawn from a container in such a way that the first marble drawn is replaced before selecting the second marble. Does the outcome of the first draw affect the outcome of the second?

a)

Yes

b)

No

68.

A bag contains some red-colored and some blue-colored marbles. First a red-colored marble is drawn and then, without replacing the first marble, a blue-colored marble is drawn. Are the two events dependent or independent?

a)

Independent

b)

Dependent

69.

There are 6 red marbles, 5 green marbles, and 4 yellow marbles in a bag. If Joe picks 2 marbles one after the other without replacement, then what is the probability that both are red in color?

a)

2/5

b)

1/21

c)

4/25

d)

1/7

70.

There are 10 pens and 15 pencils in a box. If a student selects two of them at random, then what is the probability of selecting a pen and then a pencil?

a)

7/12

b)

1/2

c)

1/4

d)

11/12

71.

The table above shows the number of cell phones per household in a small town. Find the standard deviation. Round to the nearest hundredth.

a)

0.80

b)

1.70

c)

1.30

d)

1.00

72.

a)

Yes, because all of the probabilities are between 0 and 1 inclusive and the sum of all the probabilities is 1.

b)

No, all probabilities are not be between 0 and 1 inclusive

c)

No, the sum of all the probabilities is not 1.

d)

Yes, because the distribution is symmetric

73.

A marketing survey compiled data on the number of cars in households. If X = the number of cars in a randomly selected household, and we omit the rare cases of more than 5 cars, then X has the following probability distribution:
X 0 1 2 3 4 5
P(X) 0.24 0.37 0.20 0.11 0.05 0.03
What is the probability that a randomly chosen household has at least two cars?

a)

0.20

b)

0.29

c)

0.39

d)

0.61

74.

If two coins are tossed, which is NOT a possible value of the random variable for the number of heads?

a)

0

b)

1

c)

2

d)

3

75.

By using Binomial/ Poisson Statistical Table $P\left(X\ge r\right)$ , how to find $P\left(X\le14\right)$ ?

a)

$1-P\left(X\ge15\right)$

b)

$1-P\left(X\le15\right)$

c)

$1-P\left(X\ge14\right)$

d)

$1-P\left(X\le14\right)$

76.

Find mean of Binomial Distribution?

a)

np

b)

npq

c)

nq

d)

1-q

77.

When rolling two dice, the probability of rolling doubles is ⅙. Suppose that a game player rolls the dice five times, hoping to roll doubles. What is the probability the player gets doubles less than three times in 5 attempts?

a)

0.161

b)

0.965

c)

0.015

d)

0.997

78.

If the values of the random variable X are 0,1,2 and 3 where X represents the number of heads in tossing a coin thrice, what is the probability that three heads will come up?

a)

1/2

b)

3/8

c)

1/4

d)

1/8

79.

Which of the following is NOT a requirement of a discrete probability distribution?

a)

The sum of the values for the random variable x must add up to 1.

b)

There is a discrete numerical (not categorical) random variable x, and its number values are associated with corresponding probabilities.

c)

The sum of the probabilities must all add up to 1.

d)

Every individual probability must have a value between 0 and 1 inclusively.

80.

Only 4% of people have type AB blood. What is the probability the first person with AB blood at the blood drive will be the 12th donor?

a)

.0001

b)

.0255

c)

.6382

d)

.2553

81.

Which of the following is NOT an assumption of the Binomial distribution?

a)

All trials must be independent.

b)

Each trial must be classified as a success or a failure.

c)

All trials are dependent on each other.

d)

The number of successes in the trials is counted.

82.

An algebra 2 test has 6 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 6 questions, what is the probability that you get exactly 3 questions correct?

a)

0.962

b)

0.132

c)

0.831

d)

0.250

83.

Bob is taking a 100 question test. They have a 90 % probability of getting any one question correct. WHICH IS THE CORRECT FORMULA TO FIND OUT THE PROBABILITY that they will answer EXACTLY 70 questions correctly?

a)

₁₀₀C₇₀ ( 0.18 )³⁰ ( 0.90 )⁷⁰

b)

₁₀₀C₇₀ ( 0.10 )³⁰ ( 0.90 )⁶⁰

c)

₁₀₀C₇₀ ( 0.10 )³⁰ ( 0.90 )⁷⁰

d)

₉₉C₇₀ ( 0.10 )³⁰ ( 0.90 )⁷⁰

84.

Suppose we draw 4 cards from a pack of 52 cards. What is the probability of getting exactly 3 kings?

a)

0.9999

b)

0.9997

c)

0.0007

85.

The mean number of accidents per month at a certain intersection is 3.What is the probability that in any given month exactly 4 accidents will occur at this intersection?

a)

0.081

b)

0.672

c)

0.168

86.

If A and B are any two events of a sample space S, then

a)

P (A $\cup$ B) = P (A) + P (B) – P (A $\cap$ B)

b)

P (A $\cup$ B) = P (A) + P (B) + P (A $\cap$ B)

c)

P (A $\cap$ B) = P (A) + P (B) +P (A $\cup$ B)

d)

P (A / B) = P (A) - P (B) – P (A $\cap$ B)

87.

1. If A and B are disjoint events P (A $\cup$ B) = __________.

a)

P (A) + P (B)

b)

P (A) – P (B)

c)

P (A) P(B)

d)

P (A) + P (A $\cap$ B)

88.

1. If A and B are events of a sample space S such that A ⊆ B then

a)

P (A) = P (B)

b)

P (A) < P (B)

c)

P (A) $\le$ P (B)

d)

P (A) $\ne$ P (B)

89.

1. If A and B are two events with P (A) = 0.4, P (B) = 0.3 and P (A $\cap$ B) = 0.2. Find P (A $\cup$ B)

a)

0.5

b)

0.8

c)

0.1

d)

0.2

90.

If $A_i\cap A_j\ =\ \phi$ for all i, j with i ≠ j then the sequence of subsets is said to be __________.

a)

Mutually disjoint

b)

Exhaustive

c)

Independent

d)

not Independent

91.

1. Two dice numbered as 1,2, ……,6 on their faces are thrown. Let A be the event that the sum of the numbers on the faces shown is odd and B be the event that at least one number is 1. Then P (A $\cap$ B) = __________.

a)

1/2

b)

1/3

c)

1/6

d)

2/6

92.

Two dice numbered as 1,2, ……,6 on their faces are thrown. Let A be the event that the sum of the numbers on the faces shown is odd and B be the event that at least one number is 1. Then P (A $\cup$ B) = __________.

a)

25/26

b)

23/26

c)

29/26

d)

5/6

93.

Let A and B be two events with P (B) ≠ 0. A is said to be independent of

B if P (A|B) = __________.

a)

P (A)

b)

P (A) P (B)

c)

P (B)

d)

P (A $\cup$ B)

94.

Say True or False.

If A and B are independent events then A and are also independent.

a)

True

b)

False

95.

If A, B, C are mutually independent events then

a)

A $\cup$ B and B $\cup$ C are independent

b)

A $\cap$ B and A $\cap$ C are independent

c)

A and B $\cap$ C are independent

d)

A $\cup$ B and C are independent

96.

If F(x) is a distribution function of the random variable X and if a<b then P(a<X≤b) is

a)

P(a)

b)

P(b)

c)

F(b) - F(a)

d)

F(a) - F(b)

97.

Mathematical expectation is also called as

a)

variance of a random variable (discrete only)

b)

variance of a random variable (continuous only)

c)

standard deviation of a random variable (continuous only)

d)

mean of a random variable (discrete or continuous)

98.

If a random variable takes countable number of values x₁, x₂, ….xₙ… it is called as (a) .

99.

Mathematical expectation is

a)

absolutely divergent

b)

absolutely convergent

c)

convergent

d)

divergent

100.

Say True or False.

Let X be a continuous random variable taking the values in the interval (-∞, ∞). Let f(x) be a function then $\int_{-\infty}^{\infty}f\left(x\right)\ =\ 0$

a)

True

b)

False

101.

If X is a continuous random variable, the probability of every set consisting of a single point is

a)

0

b)

1

c)

$\infty$

d)

$-\infty$

102.

The probability density function of the continuous random variable X is got by __________________ the distribution function F(x) of X.

a)

adding

b)

differentiating

c)

integrating

d)

subtracting

103.

Choose the correct option by reading the statements about Mathematical expectation

(i) E(c)=c is where is a constant (ii) E(c X) = c E(X) where c is a constant

(ⅲ)E(X+Y) =E(X). E(Y) (ⅳ) E(XY)=E(X)+E(Y)

a)

All the four statements are true

b)

Only (iii) and (iv) are true.

c)

Only (i) and (ii) are true.

d)

All the four statements are false.

104.

The concept of _____________arises when we deal with variables like heights, weights, temperature which can take any value between certain limits.

a)

continuous random variable

b)

discrete random variable

105.

A random variable X is said to be a continuous random variable if it can take any value in an interval which may be _______________ or ________________.

(a)

106.

If X is a Poisson variable with P(X=3) = P(X=4) then P(X=0) is...........

a)

0.183

b)

0.0183

c)

0.00183

d)

1.0183

107.

Say true or false : M_{X= -a} (t) = e^at M_X (t) .

a)

True

b)

False

108.

If X is a Poisson variate with P( X = 0) = P (X = 1) = c, then the value of c is

a)

e

b)

-e

c)

1/e

d)

-1/e

109.

Variance of the Poisson distribution is ...........

a)

1/λ

b)

λ²

c)

1/ λ²

d)

λ

110.

M.g.f. of Poisson distribution about the origin is --------

a)

$e^{\lambda\left(e^t-1-t\right)}$

b)

$e^{\lambda\left(e^{it}-1\right)}$

c)

$e^{\lambda\left(e^t-1\right)}$

d)

$e^{\lambda\left(e^{it}-1-t\right)}$

111.

The mean of the Poisson distribution whose p.d.f is P(x) = $\ \ \ \ \frac{e^{-\left(0.5\right)}\left(0.5\right)^x}{x!}$ is ………..

a)

- 0.5

b)

-0.05

c)

0.5

d)

0.05

112.

If X is a Poisson variate with parameter 1, P( 3 < X < 5 ) = …………..

a)

0.0153

b)

0.0183

c)

0.0163

d)

0.0172

113.

If the mean and variance of a Binomial distribution are 4 and 8/3 respectively,

then its mode is

a)

4.3

b)

3

c)

3.4

d)

4

114.

M.g.f of a binomial distribution about the origin is …….

a)

$\left(p+qe^t\right)^n$

b)

$\left(p+qe^{it}\right)^n$

c)

$\left(q+pe^t\right)^n$

d)

$\left(p+q\right)^n$

115.

M.g.f about the mean np of a binomial distribution is………………

a)

$\left(qe^{-pt}+pe^{qt}\right)^n$

b)

$\left(qe^{pt}+pe^{-qt}\right)^n$

c)

$\left(qe^{-t}+pe^t\right)^n$

d)

$\left(qe^{-pt}+pe^{qt}\right)^{ }$

116.

The mode of a binomial distribution B( 7, 1/4) is ……….

a)

1

b)

2

c)

1 and 2

d)

2 and 3

117.

If the m.g.f of a random variable X is of the form M_X(t) = $\left(0.4e^t+0.6\right)^8$ then

E(X) = ……………

a)

3

b)

3.1

c)

3.2

d)

3.3

118.

If the probability of defective bolt is 1/10 then the coefficient of skewness based

on moments is ........

a)

0.018

b)

0.18

c)

0.81

d)

0.081

119.

The Characteristic function of binomial distribution = …………

a)

$\left(q+pe^t\right)^n$

b)

$\left(q+pe^{it}\right)^n$

c)

$\left(p+qe^{it}\right)^n$

d)

$\left(q+pe^{-it}\right)^n$

120.

Find the first three moments of the binomial distribution

a)

1.68, 4.2, 0.336

b)

4.2, 1.68, -0.336

c)

0.336, 4.2, 1.68

d)

0, 1.68, -0.336

121.

M.g.f about the origin of the normal distribution is ............

a)

$e^{\mu t+\frac{\left(t^2\sigma^2\right)}{2}}$

b)

$e^{\mu t+\left(t^2\sigma^2\right)}$

c)

$e^{\frac{\left(t^2\sigma^2\right)}{2}}$

d)

$e^{\frac{t^2}{2}}$

122.

For the normal distribution, $\mu_{2n+1}$ = ----- for n = 1,2,….

a)

1

b)

1/2

c)

-1

d)

0

123.

In a normal distribution, the value of $\beta_2$ is given by

a)

0

b)

3

c)

2

d)

1

124.

The mean and standard deviation of the normal distribution f(x) = $Ke^{-\left(\frac{1}{2}\right)\left[\frac{\left(x^2+8x+16\right)}{4}\right]}$

are respectively

a)

-4, 2

b)

-4, 4

c)

-4, $\sqrt[]{2}$

d)

4, $-\sqrt[]{2}$

125.

Say true or false:

All the even order moments about mean of the normal distribution is zero.

a)

True

b)

False

126.

While Tim is waiting for class to start, he pulls a quarter from his pocket. How many outcomes are possible if he flips the quarter 3 times?

a)

3

b)

6

c)

12

d)

8

127.

What is the probability of getting an odd number on the first roll and less than 3 on the second roll?

a)

1/6

b)

2/6

c)

3/5

d)

3/6

128.

Based on the chart, what is the experimental probability of pulling a green marble?

a)

1/8

b)

8/25

c)

8/100

d)

7/8

129.

A spinner has 8 equal regions. Each region is marked with one of the following numbers: 10, 20, 30, 40, 50, 60, 70, 80. What is the probability of an even number being spun on the first roll?

a)

1/8

b)

1/2

c)

1

d)

3/8

130.

Bag A contains 9 red marbles and 3 green marbles. Bag B contains 9 black marbles and 6 orange marbles. Find the probability of selecting one green marble from bag A and one black marble from bag B.

a)

3/20

b)

1/4

c)

3/31

d)

2/27

131.

A box contains 5 purple marbles, 3 green marbles and 2 orange marbles. Draws are made without replacement.P(both marbles are purple)

a)

2/9

b)

1/3

c)

1/2

d)

1/4

132.

Kevin is making an omelet. There are 7 types of meat and 2 types of cheese to choose from. How many different omelets can Kevin make using exactly one of each item?

a)

7

b)

14

c)

9

d)

24

133.

Alvin rolls a fair 6-sided die.

What is P(roll greater than 6)?

(a)

134.

Let X and Y be the following sets:

P(X) = {5, 10, 15}

P(Y) = {3, 6, 9, 12, 15}

Which of the following is the set X U Y?

a)

{5, 10, 15}

b)

{3, 6, 9, 12, 15}

c)

{}

d)

{3, 5, 6, 9, 10, 12, 15}

135.

Let X and Y be the following sets:

X = {121, 144, 169}

Y = {11, 12, 13, 121, 144, 169}

Which of the following is the set X ∩ Y?

a)

{121, 144,169}

b)

{11, 12, 13, 121, 144, 169}

c)

{}

d)

{11, 12, 13}

136.

Three events occur with probabilities P(E₁) = 0.35, P(E₂) = 0.15, P(E₃) = 0.40. If the event B occurs, the probability becomes P(E₁|B) = 0.25, P(B) = 0.30. Calculate P(E₁ or B).

a)

0.075

b)

0.575

c)

0.021

d)

0.475

137.

Drake Marketing and Promotions has randomly surveyed 200 men who watch professional sports. The men were separated according to their educational level (college degree or not) and whether they prefer the NBA or the National Football League (NFL). The results of the survey are shown:

What is the probability that a randomly selected participant prefers NFL?

(a)

138.

A bag has 2 black and 3 red marbles. You reach into the bag, select a marble and then replace it. What is P(red, then red)?

a)

9/25

b)

1/9

c)

3/10

d)

1/72

139.

The probability model based on experimental probability for randomly selecting a marble from a bag is P(green) = $\frac{18}{40}$ , P(blue) = $\frac{14}{40}$ , and P(white) = $\frac{8}{40}$ . If there are 60 total marbles in the bag, how many would you expect to be white?

(a)

140.

The results of a survey asking 500 people about their favorite ice cream flavor are shown in the table. Find P(strawberry) as a percentage.

(a)

141.

In a certain community, 30% of households have 1 child, 43% have 2 children, and 27% have 3 children. If a household is selected at random, what is the expected number of children in that household? HINT: A Probability table may be helpful.

a)

2.00

b)

2.13

c)

1.97

d)

1.27

142.

Find the expected value

a)

Loss of $0.875

b)

Loss of $2.125

c)

Win of $1.875

d)

Win of $3.125

143.

You spin each spinner once. You get $50 if you spin a 2 and a vowel. You get $25 if you spin a 2 and a consonant. You get $5 if you spin a 1 and a vowel. Everything else earns $0. What is the expected value of this game?

a)

$80

b)

$8.75

c)

$10.25

d)

$12.50

144.

Your business is looking into looking into three contracting firms. Based on previous research, there is a 75% chance that company 1 will earn you $40,000. There is a 45% chance that company 2 will earn you $60,000. Company 3 has a 30% chance of earning you $80,000. It costs $20,000 to draw up legal paperwork for each company. How much profit or loss would you expect after this deal is done?

a)

$81,000 profit

b)

$81,000 loss

c)

$21,000 profit

d)

$21,000 loss

145.

Kevin is at a charity fundraiser and has a chance of receiving a gift. The odds in favor of receiving a gift are 6/17. Find the probability of Kevin receiving a gift.

a)

6/23

b)

17/23

c)

17/6

d)

23/6

probability theory

Total questions: 145

Worksheet time: 5hrs 59mins

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