Free Printable random variables

1.

A random variable is defined by a rule that assigns a _______________ to every outcome in a sample space.

a)

number

b)

letter

c)

Event

d)

probability

2.

Two fair dice are rolled and the numbers that appear are added. What is the probability that this sum is at least 5?

a)

5/12

b)

5/36

c)

5/6

d)

1/6

3.

A fair coin is flipped three times. What is the probability of seeing heads exactly once?

a)

3/8

b)

1/8

c)

1/2

d)

1/6

4.

The Sum Rule states that the sum of the probabilities of all instances of a random variables equals...

a)

1

b)

0

c)

P(E)

d)

P(E')

5.

Two fair dice are rolled and the numbers that appear are added. What is the probability that this sum is exactly 3?

a)

1/12

b)

1/18

c)

1/4

d)

1/6

6.

Let set A = {1, 2, 3, 4} and set B = {2, 3, 5, 7}. One number is chosen at random from each set and their sum is calculated.

What is the probability that this sum is exactly 6?

a)

3/16

b)

3/8

c)

1/16

d)

1/4

7.

Let set A = {1, 2, 3, 4} and set B = {2, 3, 5, 7}. One number is chosen at random from each set and their sum is calculated.

What is the probability that this sum is less than 6?

a)

5/16

b)

3/8

c)

5/8

d)

1/3

8.

The set of all outcomes assigned a given number, or that number itself, is called a/an __________________ of a random variable

a)

instance

b)

outcome

c)

result

d)

sum

9.

If a fair coin is tossed twice, what is the probability of seeing heads exactly once?

a)

3/4

b)

1/3

c)

1/2

d)

2/3

10.

Review: A trial consists of flipping five coins. What is the size of the resulting sample space?

a)

5

b)

10

c)

25

d)

32

11.

Integration: Consider the dot plot shown. A trial consists of selecting a single student at random from this sample. Let "x" = the number of candy bars this student sold.

Find P(x>2) :

a)

4/5

b)

3/5

c)

2/5

d)

2/15

12.

Integration: Consider the dot plot shown. A trial consists of selecting a single student at random from this sample. Let "x" = the number of candy bars this student sold.

Find P(x=2) :

a)

1/15

b)

2/15

c)

1/8

d)

1/4

13.

A bag contains five blue marbles, four yellow marbles and three green marbles.

A trial consists of drawing two marbles from this bag at random and with replacement. Let "b" = number of blue marbles drawn. Find P(b=1).

a)

0.2431

b)

0.4861

c)

0.2652

d)

0.5303

14.

A bag contains five blue marbles, four yellow marbles and three green marbles.

A trial consists of drawing two marbles from this bag at random and without replacement. Let "b" = number of blue marbles drawn. Find P(b=1).

a)

0.2431

b)

0.4861

c)

0.2652

d)

0.5303

15.

A hockey team has an equal chance of winning, losing or tying any given game. A win earns the team three points, a loss no points, and a tie one point in the standings.

What is the probability that after two games this team has at least four points in the standings?

a)

1/3

b)

1/4

c)

2/9

d)

1/8

16.

In a small town of 100 households, 29 own no dogs, 38 own one dog, 22 own two dogs, and 11 own three dogs.

Two different households are picked at random. Let "x" = the total number of dogs these two households own. Find P(x>2).

a)

0.4244

b)

0.4202

c)

0.4278

d)

0.4235

17.

Two fair dice are rolled. Let "x" = the sum of the numbers that appear on the dice.

Which value of "x" is most likely?

a)

6

b)

7

c)

3

d)

3.5

18.

Find the value of k

a)

¹/₁₅

b)

¹/₅

c)

¹/₁₀

d)

¹/₁₄

19.

Find the value of k

a)

¹/₁₅

b)

¹/₁₆

c)

¹/₁₇

d)

¹/₁₄

20.

Find P(X = 2)

a)

⁵/₃₆

b)

¹/₁₂

c)

¹/₃₆

d)

¹/₉

21.

Find P(X = 3)

a)

⁵/₃₆

b)

¹/₁₂

c)

⁷/₃₆

d)

¹/₆

22.

Find P(X = 5)

a)

¹¹/₃₆

b)

¹/₄

c)

⁵/₁₈

d)

¹/₉

23.

Find the value of q

a)

0.85

b)

0.15

c)

0.25

d)

0.05

24.

Find P(X < 5)

a)

0.2

b)

0.3

c)

0.5

d)

0.7

25.

Find P(X ≤ 5)

a)

0.2

b)

0.3

c)

0.5

d)

0.7

26.

Which statement is true?

a)

5a + b = 1

b)

6a + b = 1

c)

5a + 2b = 1

d)

7a + b = 1

27.

Find a if b = 0.4

a)

0.1

b)

0.2

c)

0.4

d)

0.6

28.

Find the value of k

a)

¹/₆

b)

¹/₁₄

c)

¹/₁₁

d)

¹/₁₅

29.

Find the value of a

a)

¹/₂

b)

¹/₄

c)

¹/₅

d)

¹/₁₀

30.

Find the value of k

a)

¹/₁₀

b)

¹/₆

c)

¹/₁₂

d)

¹/₈

31.

Find the value of p

a)

0.9

b)

0.1

c)

0.3

d)

0.15

32.

Find the value of c

a)

0.8

b)

0.2

c)

0.3

d)

0.1

33.

Which of the following random variables is NOT continuous?

a)

Amount of gasoline in a car.

b)

Time it takes to commute to work.

c)

Number of goals scored by a hockey team.

d)

Lifetime of a AAA battery.

34.

Find the value of k

a)

1

b)

1/2

c)

1/9

d)

1/10

35.

Find P(X ≤ 3)

a)

1/4

b)

1/3

c)

1/5

d)

1/9

36.

Find P(X < 2/3)

a)

32/9

b)

24/27

c)

32/81

d)

17/9

37.

Find $P\left(X=3\right)$

a)

$\frac{1}{15}$

b)

$\frac{1}{5}$

c)

$\frac{4}{15}$

d)

$\frac{3}{15}$

38.

Find $P\left(X<3\right)$

a)

$\frac{1}{15}$

b)

$\frac{1}{5}$

c)

$\frac{4}{15}$

d)

$\frac{3}{15}$

39.

Find $P\left(X\ge3\right)$

a)

$\frac{2}{15}$

b)

$\frac{2}{5}$

c)

$\frac{4}{5}$

d)

$\frac{3}{15}$

40.

Find $P\left(2<X<5\right)$

a)

$\frac{7}{15}$

b)

$\frac{2}{5}$

c)

$\frac{4}{5}$

d)

$\frac{3}{15}$

41.

Find $P\left(X\le2\right)$

a)

$\frac{1}{5}$

b)

$\frac{2}{5}$

c)

$\frac{3}{5}$

d)

$\frac{4}{5}$

42.

Find $P\left(X>2\right)$

a)

$\frac{4}{5}$

b)

$\frac{2}{5}$

c)

$\frac{1}{5}$

d)

$\frac{1}{3}$

43.

Find $P\left(2\le X<5\right)$

a)

$\frac{7}{15}$

b)

$\frac{4}{5}$

c)

$\frac{3}{5}$

d)

$\frac{14}{15}$

44.

Find $P\left(2<X<5\right)$

a)

$\frac{4}{5}$

b)

$\frac{14}{15}$

c)

$\frac{7}{15}$

d)

$\frac{3}{5}$

45.

Find the value of $k$

a)

$\frac{1}{24}$

b)

$24$

c)

$12$

d)

$\frac{1}{12}$

46.

Find $E\left(X\right)$

a)

3.3158

b)

4.2917

c)

4.3617

d)

2.2618

47.

If $E\left(X\right)=4.2917\$ find $Var\left(X\right)$

a)

3.3158

b)

2.2896

c)

4.3617

d)

2.2618

48.

Given

E\left(X\right)=\frac{41}{36}

and

E\left(X^2\right)=\frac{571}{405}

, find

Var\left(2X+2\right)

a)

0.1128

b)

0.4512

c)

0.4452

d)

0.3625

49.

If $E\left(X\right)=\frac{41}{36},$ , find $Var\left(X\right)$

a)

$0.2236$

b)

$0.1128$

c)

$\frac{571}{405}$

d)

$\frac{35}{36}$

50.

Find $E\left(X\right)$

a)

$\frac{2}{36}$

b)

$\frac{41}{36}$

c)

$\frac{3}{2}$

d)

$\frac{35}{36}$

random variables

Total questions: 50

Worksheet time: 56mins

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