Probability Bridge Course

Multiple Choice

A card is drawn at random from a deck of cards. Find the probability of getting a queen.

• 1/52

• 5/52

• 1/13

• 1/26

Multiple Choice

0!

• 1

• 0

• 10

• undefined

Multiple Choice

A player rolls a die and receives the same number of Rupees as the number of dots on the face that turns up. What should the player pay for ticket for each roll if he wants to make a profit of 1 rupees per throw of die in the long run ?

• 2.5 rupees

• 2 rupees

• 3.5 rupees

• 3 rupees

Multiple Choice

When 4 dice are rolled together, the probability that exactly one dice shows the number '5' is

• 125/1296

• 125/324

• 15/1296

• None of these

Multiple Choice

Say 'TRUE' or 'FALSE'
In any situation that has only two outcomes, each outcome will be probability ½

• TRUE

• FALSE

Fill in the Blank

Alvin rolls a fair 6-sided die.

What is P(roll greater than 6)?

Multiple Choice

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?

• 5/6

• 1/2

• 1/3

• 1/6

Multiple Choice

What is the probability of impossible event?

• 1

• 0

• Insufficient data

• Not defined

Multiple Choice

The value of probability lies between which two numbers?

• 2 to 5

• 0 to 1

• 1 to 2

• 1 to 6

Multiple Choice

What is an outcome?

• The result of an experiment

• The chance or likelihood of an event

• A fraction, decimal, or a percent

• An activity that gives various results

Multiple Choice

Probability can be written as a 

• fraction

• percent

• decimal

• all of the above

Multiple Choice

A card is drawn at random from a deck of cards. Find the probability of getting the 3 of diamond?

• 1/52

• 4/52

• 1/13

• 1/26

Multiple Choice

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

• 1/3

• 1/6

• 1/2

• 1/4

Multiple Choice

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?

• 3
• 1/10
• 3/10
• 30%

Multiple Choice

Find the probability of rolling a 7 on a single die.

• 0

• 1/6

• 2/3

• 1

Multiple Choice

The range of the data 8, 8, 8, 8, 8 . . . 8 is

• 0

• 1

• 8

• 3

Multiple Choice

The letters that form the word ALGEBRA are placed in a bowl. What is the probability of choosing a letter other than “A”? 

• 5/7

• 2/7

• 5/49

• 10/49

Multiple Choice

The letters that form the word MATHEMATICS are placed individually in a bowl. When selecting a letter from the bowl, what is the probability of choosing a vowel?

• 16/121

• 4/11

• 3/11

• 5/11

Multiple Choice

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

P (NOT lime)

• 7/10

• 3/10

• 30%

• no answer

Multiple Choice

The probability of event equal to zero is called

• Unsure event

• Sure event

• Impossible event

• None of these

Multiple Choice

Marvin has a standard deck of cards.

P (Ace or 5)

• 2/13

• 1/13

• 10/13

• 1/52

Multiple Choice

What is the probability of getting any letter that is not A?

• 6/8
• 3/4
• 2/8
• 1/4

Multiple Choice

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?

• 5/6

• 1/3

• 1/2

• 1/6

Multiple Choice

The sum of all deviations of the data from its mean is

• Always positive

• Always negative

• zero

• non-zero integer

Multiple Choice

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

• 5/26

• 1/26

• 2/26

• 7/21

Multiple Choice

What is the probability of spinning the spinner and landing on the 7?

• impossible
• equally likely 
• unlikely 
• very likely 

Multiple Choice

Experimental Probability is:

• What actually happens

• What I think Happens

• What should happen

• What Will happen 

Multiple Choice

What is the probability of getting 4 on a die?

• 1

• 1/2

• 1/5

• 1/6

Multiple Choice

An unprepared student takes a 3-question true/false quiz in which he guesses the answers to all 3 questions. What is the probability he gets all 3 correct?

• 1/8

• 1/3

• 1/2

• 1/6

Multiple Choice

A probability near 1 is _______.

• never going to happen 
• very likely to happen
• probably never going to happen
•  equally likely to happen

Multiple Choice

You give the answer to a probability problem as 6/5. The teacher marks it wrong. Why?

• Its more than 1.

• It should have been 5/6.

• Its not written as a percent.

• Its not written as a decimal.

Multiple Choice

The mean of 100 observations is 40 and their standard deviation is 3. The sum of squares of all deviations is

• 40000

• 160900

• 160000

• 30000

Multiple Choice

Which of these cannot be considered a probability of an outcome?

• 0

• -1/5

• 1

• 100

Multiple Choice

Probability can be expressed as a number between_____ and _____.

• 0 and 100
• 0 and 10
• 0 and 1
• -1 and 1

Multiple Choice

Roll a die one time. Find P(rolling a 4).

• 1/6

• 1/3

• 2/3

• 2/3

Multiple Choice

A card is drawn from the set of 52 cards. The probability of getting a queen is

• 1/26

• 1/13

• 4/53

• 4/13

Multiple Choice

Roll a die one time. Find P(even number).

• 1/2

• 1/6

• 3/6

• 1/3

Multiple Choice

Probability can be written as ...

• a fraction
• a decimal
• a percent
• all of the above

Multiple Choice

Roll a die one time. Find P(a number greater than 3 or odd).

• 5/6

• 0

• 1/2

• 1/6

Multiple Choice

Variance of first 20 natural numbers is

• 32.25

• 44.25

• 33.25

• 30

Multiple Choice

Draw one card from a standard deck. Find P(ace)

• 4/52

• 1/13

• 4/13

• 2/52

Multiple Choice

What is an event that will happen or has a probability of 1?

• theoretical

• probability

• mutually exclusive

• certain

Multiple Choice

Draw one card from a standard deck. Find P(diamond)

• 25%

• 50%

• 15%

• 75%

Multiple Choice

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?

• 3
• 1/10
• 3/10
• 30%

Multiple Choice

Draw one card from a standard deck. Find P(ace of diamonds)

• 1/52

• 1/4

• 1/13

• 4/13

Multiple Choice

outcome with the same chance of occurring

• mutually exclusive

• impossible

• equally

• independent

Multiple Choice

Draw one card from a standard deck. Find P(4 or club)

• 4/13

• 7/52

• 2/13

• 1/26

Multiple Choice

The standard deviation of a data is 3. If each value is multiplied by 5 then the new variance is

• 3

• 15

• 5

• 225

Multiple Choice

What is the probability that you choose blue? simplify your answer

5 green

6 yellow

8 blue

7 brown

• 4/13

• 8/26

• 8/25

• 1/3

Multiple Choice

an event with a probability of zero

• impossible

• mutually exclusive

• outcome

• outcome

Multiple Choice

P(not A) = 
*Remember to simplify.*

• 6/8
• 3/4
• 2/8
• 1/4

Multiple Choice

Possible results of an event

• outcomes
• compound event
• simple event
• probability

Multiple Choice

If the standard deviation of x, y, z is p then the standard deviation of 3x + 5 , 3y + 5 , 3z + 5 is

• 3p + 5

• 3p

• p + 5

• 9p + 15

Multiple Choice

The probability of an event is written as P(event).

• False
• True

Multiple Choice

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?

• 3

• 1/10

• 3/10

• 30%

Multiple Choice

In a deck of cards, there are _______ non-face cards.

• 40

• 52

• 48

• 12

• 36

Multiple Choice

If the mean and coefficient of variation of a data are 4 and 87.5% then the standard deviation is

• 3.5

• 3

• 4.5

• 2.5

Multiple Choice

# of favorable outcome divided by the total possible outcomes

• Percent
• Probability
• Sample Space
• Chance

Multiple Choice

The letters that form the word MATHEMATICS are placed in a bowl. What is the probability of choosing a letter that is a vowel?

• 7/11

• 4/11

• 2/11

• 5/26

Multiple Select

Which of the following is incorrect?

• P (A) > 1

• 0 ≤ P (A) ≤ 1

• P(ɸ) = 0

• P (A) + P (A^-) = 1

Fill in the Blank

Ahmed spins the spinner shown below once. Each sector shown has an equal area.

What is P(shaded area)?

Multiple Choice

The probability a red marble selected at random from a jar containing p red, q blue and r green marbles is

Multiple Choice

What is an outcome?

• The result of an experiment
• The chance or likelihood of an event
• A fraction, decimal, or a percent
• An activity that gives various results

Multiple Choice

A page is selected at random from a book. The probability that the digit at units place of the page number chosen is less than 7 is

• 3/10

• 7/10

• 3/9

• 7/9

Multiple Choice

What is the probability of flipping a coin

3 times and getting 3 heads?

• 1/8

• 1/4

• 1/2

• 3/4

Multiple Choice

The probability of getting a job for a person is x/3 . If the probability of not getting the job is 2/3 then the value of x is

• 2

• 1

• 3

• 1.5

Multiple Choice

A set of all possible outcomes is known as - 

• a list
• a complement
• a sample space
• an event

Multiple Choice

Kamalam went to play a lucky draw contest. 135 tickets of the lucky draw were sold. If the probability of Kamalam winning is 1/9 , then the number of tickets bought by Kamalam is

• 5

• 10

• 15

• 20

Multiple Choice

Probability is ...

• the chance that some event will occur.
• a game that involves coins.
• a guarantee.

Multiple Choice

If a letter is chosen at random from the English alphabets {a,b,...,z}, then the probability that the letter chosen precedes x

• 12/13

• 1/13

• 23/26

• 3/26

Multiple Choice

What is the probability of selecting an orange candy?

• 0%
• 25%
• 50%
• 100%

Multiple Choice

A purse contains 10 notes of ₹2000, 15 notes of ₹500, and 25 notes of ₹200. One note is drawn at random. What is the probability that the note is either a ₹500 note or ₹200 note?

• 1/5

• 3/10

• 2/3

• 4/5

Multiple Choice

You roll two die.

What is the probability you will roll a 4, then roll a number less than 3?

• 1/36

• 1/18

• 1/9

• 1/6

Multiple Choice

What is the probability of flipping a coin

3 times and getting 3 heads?

• 1/8

• 1/4

• 1/2

• 3/4

Multiple Choice

If an event cannot occur, then its probability is 

• 1
• ½
• ¼
• 0

Multiple Choice

A regular deck contains 52 cards, 2 of which are red eights. Assuming the cards are dealt randomly, which is the probability that the first card dealt will be a red eight?

• 1/26
• 1/13
• 1/52
• 2/13

Multiple Choice

Lucy has the spinner pictured and spins it twice in a row. What is the probability that she lands on blue first and then on yellow or green?

• 1 / 16

• 1 ⁄ 6

• 1 ⁄ 8

• 3 ⁄ 4

Multiple Choice

Probability can be written as ...

• a fraction
• a decimal
• a percent
• all of the above

Fill in the Blank

Adam flips a fair coin.

What is P(Heads)?

Multiple Choice

A bag contains 1 red marble, 2 blue marbles, and 3 green marbles. What is the probability of picking a red marble?

• 1/6

• 1/3

• 1/5

Multiple Choice

Three cards are picked from a pack of cards. What is the probability that all the three cards are picked are of different suits?

• 169/525

• 169/425

• 169/1700

• None of these

Multiple Choice

A number is randomly selected from 0-10. What is the probability the number selected is greater than 5?

• 1/2
• 3/5
• 2/5
• 5/11

Fill in the Blank

Harry can't figure out what to eat. He is going to randomly select a piece of fruit from his pantry. There are 4 apples and 5 bananas in his kitchen.

What is P(select an apple)?

Multiple Choice

Two fair dice are thrown. What is the probability that the outcome will either total 7 or include a 3?

• 5/12

• 1/2

• 8/9

• 2/3

Multiple Choice

If E be an event  such that P(E) = 3⁄7, then P(not E) is _______

• 4⁄7
• 6⁄7
• 5⁄7
• None of these

Multiple Choice

Find the probability of drawing a 10 from a standard deck of 52 cards.

• 4 out of 52
• 13 out of 52
• 13/52
• 4/52

Fill in the Blank

Rafina roll a 6-sided die.

What is P(roll less than 4)?

Fill in the Blank

Probability of getting atleast 2 heads when 3 coins are tossed together is

Multiple Choice

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?

• {5, 10, 15}

• {3, 6, 9, 12, 15}

• {}

• {3, 5, 6, 9, 10, 12, 15}

Multiple Choice

Which of the following cannot be the probability of an event?

• 17⁄16
• 0.1
• 3%
• ⅓

Multiple Choice

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?

• {121, 144,169}

• {11, 12, 13, 121, 144, 169}

• {}

• {11, 12, 13}

Multiple Choice

There are seven nickels and eight dimes in your pocket. You randomly pick a coin out of your pocket and then return it to your pocket. Then you randomly pick another coin.  What is the probability that the coin is a dimes both times?

• 49/225

• 8/15

• 7/15

• 64/225

Multiple Select

A car salesman has noted that the probability that the dealership sells a car on a Saturday morning is 0.30. Then the probability of the dealership not selling a car on Saturday morning is 0.70.

• True

• False

Multiple Choice

Which of the following can be the probability of an event?

• -0.04
• 1.0004
• 18⁄23
• 8⁄7

Multiple Choice

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).

• 0.075

• 0.575

• 0.021

• 0.475

Multiple Choice

A set is a

• collection of objects

• collection of well defined objects

• collection of well connected objects

• well defined collection of objects

Fill in the Blank

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?

Multiple Choice

A card is selected at random from a deck of 52 cards. The probability of its being black face card is _____

• 3⁄26
• 3⁄13
• 1⁄2
• 2⁄13

Multiple Choice

A basket contains four apples and six peaches. You randomly select one of the fruit and eat it. Then you randomly select another fruit. What is the probability that both pieces of fruit are peaches?

• 2/15
• 9/15

• 9/25

• 2/25

Multiple Choice

Choose the correct answer
If P(A) denote the probability of an event A, then _____ 

• P(A) < 0
• P(A) > 1
• 0 ≤ P(A) ≤ 1
• -1 ≤ P(A) ≤ 1

Multiple Choice

• 0.89

• 0.761

• 0.841

• 0.784

Multiple Choice

A box contains 5 red, 4 green and 3 black balls.  A ball is drawn at random from the box.  The probability of drawing a green ball is____

• 4⁄12
• 4⁄11
• 4⁄10
• 4⁄9

Multiple Choice

A bag contains 5 red marbles and 8 pink marbles. A marble is randomly drawn and then replaced. What is the probability the first marble is red and the second is pink?

• 26.9%
• 24.7%
• 20.0%
• 23.6%

Multiple Choice

A bag contains 5 red, 3 green and 5 black balls. A ball is drawn at random from the bag.  Find the probability that the ball is not red

• 5⁄13
• 3⁄13
• 8⁄13
• 5⁄12

Multiple Choice

Suppose a bird lays two eggs. What is the probability that first egg hatched is a female bird and the second egg hatched is male bird?

• 1/2

• 1/3

• 1/4

• 3/4

Multiple Choice

• TRUE
• FALSE

Multiple Choice

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 neither red nor blue?

• 5/6
• 1/2
• 1/3
• 1/6

Multiple Select

Accidents occur with a Poisson Distribution at an average of 4 per week, that is, lambda=4. Then which of the following are correct ?

• The probability of more than 5 accidents in any one week is 0.215

• The probability of more than 5 accidents in any one week is 0.314

• The probability of that at least two weeks will elapse between accident is 0.00034

• The probability of that at least two weeks will elapse between accident is 0.00032

Multiple Choice

At a community swimming pool there are 2 managers, 8 lifeguards, 3 concession stand clerks, and 2 maintenance people.  If a person is selected at random, find the probability that the person is either a lifeguard or a concession stand clerks.

• 2/3
• 8/15
• 11/15

• not enough information

Multiple Select

Null set is a set with

• 1 element

• No elements

• zero elements

• zero as an element

Multiple Choice

A bag contains 6 red balls, 5 black balls and 3 white balls. Find the probability drawing three balls of same colour is

• 21/364

• 31/364

• 21/374

• None of these

Multiple Choice

A biased Die is thrown 30 times and the number of Sixes seen is 8. If the die is thrown a further 12 times find the probability that a six will occur exactly twice

• 0.29

• 0.211

• 0.256

• 0.274

Multiple Choice

If eight coins are tossed together, then find the probability of getting more heads than tails?

• 91/256

• 93/256

• 95/256

• None of these

Multiple Choice

A jar contains 3 red marbles, 7 green marbles and 10 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is white?

• 1/2

• 1/10

• 1/3

• 1/5

Multiple Choice

A problem in Maths is given to the students X, Y and Z. The probability that the problem is solved by each of the three students is 4/10, 3/7 and 5/9 respectively. Find the probability that neither of them solves the problem?

• None of these

• 14/105

• 11/105

• 16/105

Multiple Choice

• 0.451

• 0.675

• 0.399

• 0.558

Multiple Choice

A box contains nine bulbs out of which 4 are defective. If three bulbs are chosen at random, find the probability that all the three bulbs are defective?

• 1/84

• 1/94

• 1/72

• None of these

Multiple Choice

A set which contains all the elements that are common in two sets is called ___________ of sets

• Union

• Intersection

• Difference

• Subset

Multiple Choice

11 books are placed at random in a shelf. The probability that a pair of books will always be together is -.

• 3/11

• 1/2

• 4/11

• None of these

Multiple Choice

• 5/104

• 7/104

• 3/104

• 9/104

• 1/104

Multiple Choice

The probability that A speaks truth is 4/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?

• 18/35

• 19/35

• 21/35

• None of these

Multiple Choice

A jar contains 3 red marbles, 7 green marbles and 10 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is neither red nor white ?

• 1/3

• 7/20

• 1/7

• 1/2

Multiple Choice

Tickets numbered 1 to 21 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

• 1/2

• 10/21

• 9/20

• None of these

Fill in the Blank

Multiple Choice

If two letters are taken at random from the word FORMULA, what is the probability that both of the letters would be vowels?

• 1/7

• 2/7

• 4/21

• None of these

Fill in the Blank

The probability of occurrence of any event lies between _____ & ______

Multiple Choice

There are 2 bags. One has 5 white and 3 black napkins. The other one has 4 white and 8 black napkins. Find the probability of picking up a white napkin.

• 23/48

• 21/48

• 25/48

• None of these

Fill in the Blank

Suppose X is a Random Variable taking Values in {-2,-1,0,1,2,3,4,5} each with probability 1/8. Let Y=X^2. Find E[Y].

Multiple Choice

Rohit speaks the truth in 50% of cases and Y speaks the truth in 80% of cases. What is the percentage of cases that are likely to contradict each other while narrating the same event?

• 50%

• 33.33%

• 22.5%

• None of these

Multiple Choice

A bag contains 4 white counters, 6 black counters, and 1 green counter. What is the probability of drawing a black counter?

• 1/3

• 1/4

• 1/6

• 6/11

Multiple Choice

In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples ?

• 5/21

• 6/7

• 4/7

• 17/21

Fill in the Blank

Multiple Choice

fifteen persons are sitting around a circular table facing the centre. What is the probability that three particular persons sit together ?

• 3/91

• 2/91

• 1/91

• 4/91

Multiple Choice

The ways of arranging or selecting smaller or equal number of objects from a given set of objects is called

• Probability

• Permutation

• Combination

• None of the above

Multiple Choice

The letters of the word CASTIGATION is arranged in different ways randomly. What is the chance that vowels occupy the even places ?

• 0.049

• 0.034

• 0.043

• None of these

Multiple Choice

A bag contains 4 white counters, 6 black counters, and 1 green counter. What is the probability of drawing a white counter or a black counter ?

• 10/11

• 1/11

• 2/3

• 1/3

Multiple Choice

ⁿC_r ≠ ⁿC_n-r

• True

• False

Multiple Choice

The blood groups of 200 people is distributed as follows: 50 have type A blood, 65 have B blood type, 70 have O blood type and 15 have type AB blood. If a person from this group is selected at random, what is the probability that this person has O blood type?

• 0.35

• 0.40

• 0.5

• 0.2

Multiple Choice

If A⊂B, it implies that A is ___________ of B

• Super set

• Sub set

• Power Set

• Universal Set

Multiple Choice

Ritu has 3 shirts in shades of red, 4 in yellow shades and 5 in green shades. Three shirts are picked at random. The probability that all of those are in red shades is :

• 1/220

• 1/64

• 1/33

• None

Fill in the Blank

The probability of getting a tail when a coin is tossed

Multiple Choice

How many 6-digit odd numbers with distinct digits can be created using the digits 1, 2, 3, 4, 5, 6 and what is the probability of selecting such a number?

• 360, ½

• 720, 1/5

• 120, 1/6

• 360, 1/4

Fill in the Blank

Probability of A drowning in Delhi is

Multiple Choice

If the probability that A will live 15 yr is 7/8 and that B will live 15 yr is 9/10, then what is the probability that both will live after 15 yr ?

• 1/20

• 63/80

• 1/5

• None of these

Multiple Choice

The probability that a card is drawn from a pack of 52 cards will form a pack of 52 cards will be diamond or king being in?

• 4/13

• 1/210

• 8/125

• 4/25

Multiple Choice

Find the probability that a leap year chosen at random will contain 53 sundays.

• 2/7

• 3/7

• 1/49

• 1/7

Multiple Choice

A 5-digit number is formed by the digits 1,2,3,4 and 5 without repetition. What is the probability that the number formed is a multiple of 4?

• 1/4

• 1/5

• 2/5

• 1/120

Multiple Choice

A committee of three is to be chosen from a group of 3 men and 4 women.The probability of all the three being women is

• 4/35

• 3/35

• 31/35

• 34/35