Probability Questions and Answers

Q 1

A drawer holds 4 red hats and 4 blue hats. What is probability of getting exactly 3 red hats or 3 blue hats when taking out 4 hats randomly out of the drawer and immediately returning every hat to the drawer before taking out the next?


A)  

1/2

B)  

1/4

C)  

1/6

D)  

1/8


Correct Option - B

Explanation

P(getting a red hat in 1 draw)

= 4/8 = 1/2

P(getting a blue hat in 1 draw)

= 1/2

P(getting 3 red hats)

= (1/2)*(1/2)*(1/2)

= 1/8

P(getting 3 blue hats)

= 1/8

P(getting 3 red hats or 3 blue hats)

= (1/8)+(1/8)

= 1/4

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Q 2

A man who goes to work long before sunrise every morning gets dressed in the dark. In his sock drawer, he has 6 black and 8 blue socks. What is the probability that his first pick was a black sock, but his second pick was a blue sock?


A)  

24/91

B)  

12/91

C)  

12/49

D)  

24/49


Correct Option - A

Explanation

Probability of picking up a black sock first and a blue sock second

= (6/14)*(8/13)

= 24/91

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Q 3

After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?


A)  

0

B)  

12/212

C)  

11/12

D)  

1/12


Correct Option - A

Explanation

If all the other 11 letters are inserted in the correct envelopes, the 12th one should also be in the correct envelope. Hence, the probability is zero.

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Q 4

A certain jar contains 100 jelly beans: 50 white, 30 green, 10 yellow, 5 red, 4 purple, and 1 black. If a jelly bean is to be chosen at random, what is the probability that the jelly bean will be neither purple nor red?


A)  

0.09

B)  

0.11

C)  

0.55

D)  

0.91


Correct Option - D

Explanation

P(purple)

= 4/100

P(red)

= 5/100

P(neither purple nor red)

= 1-(4/100)-(5/100)

= 1-(9/100)

= 91/100

= 0.91

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Q 5

A bag contains 4 pink and 5 blue beads. Another bag contains 3 pink and 6 blue beads. Two beads are drawn, one from each bag. Find the probability that one is pink and the other is blue.


A)  

13/27

B)  

1/2

C)  

7/11

D)  

14/27


Correct Option - A

Explanation

n(S) = 9C1*9C1 = 81


No. of ways of selecting a pink and a blue bead

= [n(Pink from bag 1)*n(Blue from bag 2)]+

[n(Blue from bag 1)*n(Pink from bag 2)]

n(E) = (4*6)+(5*3)

= 39

P(E) = 13/27

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Q 6

A man who goes to work long before sunrise every morning gets dressed in the dark. In his sock drawer, he has 6 black and 8 blue socks. What is the probability that his first pick was a black sock, but his second pick was a blue sock?


A)  

24/91

B)  

12/91

C)  

12/49

D)  

24/49


Correct Option - A

Explanation

Probability of picking up a black sock first and a blue sock second

= (6/14)*(8/13)

= 24/91

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Q 7

Eric throws two dice, and his score is the sum of the values shown. Sandra throws one die, and her score is the square of the value shown. What is the probability that Sandra’s score will be strictly higher than Eric’s score? 


A)  

137/216

B)  

17/36

C)  

173/216

D)  

5/6


Correct Option - A

Explanation

definitely higher.

36+36+36 = 108 ways

If she scores 1,

Eric's score will always be greater.

If she scores 4,

her score will be higher only if Eric scores (1,1), (1,2) or (2,1)

3 ways

If she scores 9,

Eric's score will be greater if he scores (3,6), (4,5), (5,4), (6,3), (4,6), (5,5), (6,4), (5,6), (6,5), (6,6)

Eric's score will be lesser in (36-10 =)26  ways.

n(E) = 108+0+3+26

= 137

n(S) = No. of ways of throwing three dice

= 6*6*6 = 216

P(E) = 137/216

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