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Probability Questions

Home > Quantitative Aptitude > Probability > General Questions
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A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:


A1/22

B3/22

C2/91

D2/77

Answer: Option C

Explanation:

n(s)= probability of drawing three balls out off 15 balls = 15c3

                                                                                 = (15*14*13)/(3*2*1)

                                                                                 = 455

n(E) = probability of getting red ball = 5c3 

                                                      = (5*2*1)/(3*2*1)

                                                      =10

P(getting red ball)= n(E)/n(s)

                           = 10/455

                               = 2/91

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In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:


A21/46

B25/117

CJan-50

D25-Mar

ENone of these

Answer: Option A

Explanation:

Let's assume the sample space = S
and Event of selecting 1 girl and 2 boys = E

So, n(S) = Number ways of selecting 3 students out of 25 = 25C3
=> (25 * 24 * 23)/(3 * 2 * 1) = 2300.
n(E) = (10C1 * 15C2)
= 10 * [(15 * 14)/(2 * 1)] = 1050.
P(E) = n(E)/n(S) = 1050/2300 = 21/46.

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A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?


A10/21

B11/21

C2/7

D5/7

Answer: Option A

Explanation:

Answer: 10/21



Solution: 2 red, 3 green, and 2 blue balls are there. So the probability of getting no blue ball is not selecting any blue ball among the two chosen balls hence 5C2.



5C2/7C2 = 10/21.



7C2 because we can select any 2 balls from 7 balls in that number of ways.

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10 men and 10 women are there, they dance with each other, is there possibility that 2 men are dancing with same women and vice versa.


A1

B1/2

C2/3

DNever

ENone of these

Answer: Option D

Explanation:

Answer: Never



Solution: Because it is written that 10 men and 10 women dance with each other. So there is no chance of matching more than 2 partners at a time. So 2 men

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There is a toy train that can make 10 musical sounds. It makes 2 musical sounds after being defective. What is the probability that same musical sound would be produced 5 times consecutively?


A1/32

B11/32

C1/16

D11/16

Answer: Option A

Explanation:

1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32

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There are 11 boys in a family. Youngest child is a boy. Probability is 1 that of all are boys out of?


A2

B2!

C2048

D1024

Answer: Option D

Explanation:

Answer: 1/1024



Solution: 11 boys, given youngest one is the boy

Probability of a boy or girl is (1/2)

Probability of finding remaining 10 children to get a boy is-

so (1/2)^10=1/1024.

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For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A's chances of winning. Let's assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?


A1/9

B4/9

C5/9

D2/3

Answer: Option C

Explanation:

Answer: 5/9



Solution: Answer is 5/9 because for example



Let Paul picks Ghana then probability that its prophecy will be true is 2/3*2/3 =4/9.



Now it may pick up Bolivia and the chances of winning are 1/3*1/3=1/9



So total probability will be 4/9 1/9=5/9

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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?


A1/12

B0

C12/212

D11/12

Answer: Option B

Explanation:

Answer: zero



Solution:



If one letter is put in a wrong envelope, then one other letter must also be put in the wrong envelope. So zero is the probability that exactly 1 letter is inserted in an improper envelope because it's not possible.

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In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?


A1/10

B2/5

C2/7

D5/7

Answer: Option C

Explanation:

P (getting a prize) = 10/(10 + 25)
=> 10/35 = 2/7

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A 5-digit number is formed by the digits 2,4,5,6,8 (each digit used exactly once) . What is the probability that the number formed is divisible by 4 ?


A1/5

B2

C3

D2/5

Answer: Option D

Explanation:

A no. is divisible by 4 if last two digit is divisible by 4
so numbers ending with 24,28,48,52,56,64,68,84 are divisible by 4
last two places are fixed by 24,28,48,52,56,64,68,84
so remaining 3 places can be filled in 3! ways for each
total=8*3!=48=n(E)
n(S) = 5!
so
= n(E)/n(S)
=48/120=2/5

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