# Aptitude Questions: Probability Set 8

Hello Aspirants. Welcome to Online Quantitative Aptitude Section in AffairsCloud.com. Here we are creating question sample in Probability, which is common for all the  competitive exams. We have included Some questions that are repeatedly asked in bank exams !!

1. A box contains tickets numbered from 1 to 24. 3 tickets are to be chosen to give 3 prizes. What is the probability that at least 2 tickets contain a number which is multiple of 3?
A) 35/256
B) 33/220
C) 63/253
D) 43/190
E) 59/253
C) 63/253
Explanation:

From 1 to 24, there are 8 numbers which are multiple of 3
Case 1: 2 are multiple of 3, and one any other number from (24-8) = 16 tickets
8C2*16C1 / 24C3 = 56/253
Case 2: all are multiples of 3.
8C3 / 24C3 = 7/253

2. A box contains 6 blue, 5 green and 4 red balls. Two balls are drawn at random. What is the probability that there is no red ball?
A) 3/30
B) 11/21
C) 5/18
D) 11/23
E) None of these
B) 11/21
Explanation:

Total balls = 15
Not red means green or blue i.e. any of (5+6) = 11 balls
So prob. = 11C2 / 15C2

3. From a pack of 52 cards, 2 cards are drawn at random. What is the probability that both cards are black card or  heart card?
A) 31/102
B) 21/73
C) 1/5
D) 17/100
E) 3/10
A) 31/102
Explanation:

Prob. of black card:
26C2 / 52C2 = 25/102
Prob. of heart card:
13C2 / 52C2 = 3/51

4. Two cards are drawn at random from a pack of 52 cards. What is the probability that either both are black or both are jacks?
A) 62/221
B) 21/312
C) 5/21
D) 55/221
E) None of these
D) 55/221
Explanation:

There are total 26 cards black, and 4 jacks in which 2 are black jacks
So case 1: both are black
26C2/52C2
case 2: both are jack
4C2/52C2
But now 2 black jacks have been added in both cases, so subtracting their prob. : 2C2/52C2
So 325/1326 + 6/1326 – 1/1326

5. From a group of 3 men, 4 women and 2 children, 4 people are to be chosen to form a committee. What is the probability that the committee contains 1 each of men, women and children?
A) 4/15
B) 12/21
C) 4/19
D) 11/31
E) None of these
B) 12/21
Explanation:

Case 1: Prob. when 2 men, 1 woman and 1 child
3C2*4C1*2C1 /9C4 = 4/21
Case 2: Prob. when 1 man, 2 women and 1 child
3C1*4C2*2C1 /9C4 = 2/7
Case 3: Prob. when 1 man, 1 woman and 2 children
3C1*4C1*2C2 /9C4 = 2/21

6. A box contains 25 bulbs out of which 5 are defective. 3 bulbs are to be delivered to a customer. What is the probability that he get one defective bulb?
A) 19/46
B) 25/51
C) 44/77
D) 21/46
E) None of these
A) 19/46
Explanation:

5C1*20C2/25C3

7. There are 4 red balls, 5 white and 3 green balls in a basket. 3 balls are chosen at random. What is the probability that there is at most 1 green ball?
A) 13/40
B) 48/55
C) 25/68
D) 8/33
E) 9/19
B) 48/55
Explanation:

Case 1: 0 green ball means all three red or white balls
9C3/12C3
Case 2: 1 green ball and two red or white balls
9C2*3C1/12C3

8. A bag contains 3 red, 4 green and 3 yellow balls. If 2 balls are drawn at random, what is the probability that they are of different color?
A) 9/16
B) 4/15
C) 11/15
D) 5/11
E) None of these
C) 11/15
Explanation:

This will be = 1- prob.(both are same in color)
Prob. of both same in color = [3C2+4C2+3C2]/10C2 = 12/45
So required prob. = 1 – 12/45

9. There are 4 black balls and 6 white balls. 2 balls are drawn one by one without replacement. What is the probability that the balls are same in color?
A) 9/21
B) 8/17
C) 5/14
D) 7/15
E) 9/19
D) 7/15
Explanation:

When both black, prob. = 4/10 * 3/9
When both white, prob. = 6/10 * 5/9

10. A bag contains 5 red balls and 4 green balls. What is the probability that both balls are same in color?
A) 5/11
B) 4/9
C) 3/13
D) 6/17
E) None of these
B) 4/9
Explanation:

Case 1: both red
5C2/9C2
Case 2: both green
4C2/9C2