BANK & INSURANCE (PROBABILITY) PART 1

Total Questions: 45

1. A bag contains 4 green, 5 blue, 2 red and 3 yellow balls. If eight balls are drawn at random, what is the probability that there are equal number of balls of each colour?

Correct Answer: (c) 60/1001
Solution:P (of getting equal number of balls of each colour) =
(⁴C₂ × ⁵C₂ × ²C₂ × ³C₂) / ¹⁴C₈ = (6 × 10 × 1 × 3) / 3003
= 60/1001

2. In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that the student opted for NCC or NSS?

Correct Answer: (b) 19/30  
Solution:P (NCC) = 30/60 & P (NSS) = 32/60
P (NCC & NSS) = 24/60
P (NCC or NSS) = P (NCC) + P (NSS) − P (NCC & NSS)
= (30 + 32 − 24)/60 = 38/60 = 19/30

3. One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will not be an ace.

Correct Answer: (c) 12/13
Solution:P (drawing an ace card) = 4/52 = 1/13
P (not drawing an ace card) = 1 − 1/13 = 12/13

4. In a lottery, there are 10 prizes and 15 blanks in tickets. A ticket is drawn at random. What is the probability of getting a prize?

Correct Answer: (d) 2/5  
Solution:n(S) = 10 + 15 = 25
n(E) = 10
P(E) = n(E)/n(S) = 10/25 = 2/5

5. One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability that the card drawn is a red face card?

Correct Answer: (d) 3/26  
Solution:

n (red face cards) = 6
n(S) = 52
Required probability = 6/52 = 3/26

6. A bag contains 8 black balls, 5 green balls, and 2 red balls. If two balls are picked up at random, what is the probability that they are of same colour?

Correct Answer: (a) 13/35  
Solution:

Total number of balls = 8 + 5 + 2 = 15
Total number of ways in which 2 balls can be selected are = ¹⁵C₂ ways = 105
2 black balls are selected are = ⁸C₂ ways = 28
2 green balls = ⁵C₂ ways = 10

2 red balls are selected = ²C₂ ways = 1
Required probability = (28 + 10 + 1)/105 = 13/35

7. From a bag consisting 4 red balls and 5 black balls, four balls are drawn. Find the probability that at least three black balls are drawn?

Correct Answer: (a) 5/14  
Solution:Total no. of possible outcomes = ⁹C₄ = 126
Total no. of favourable outcomes = (3 Black and 1 Red) or 4 Black
= (⁵C₃ × ⁴C₁) + ⁵C₄ = 40 + 5 = 45
Required probability = 45/126 = 5/14

8. From a group of 5 females and 4 males, three persons are selected at random. Find the probability that at least two females are selected?

Correct Answer: (d) 25/42  
Solution:Total no. of possible outcomes = ⁹C₃ = 84
Total no. of favourable = 1 Male 2 Females or 3 Females
= (⁴C₁ × ⁵C₂) + ⁵C₃ = 50
Required probability = 50/84 = 25/42

9. A bag contains 4 green, 5 blue, 2 red and 3 yellow balls. If three balls are drawn at random, what is the probability that at least one is yellow?

Correct Answer: (b) 199/364  
Solution:

P (of getting at least one yellow ball) = 1 − P (of getting no yellow ball)
= 1 − (¹¹C₃ / ¹⁴C₃) = 1 − 165/364 = 199/364

10. A bag contains 7 blue balls, 9 yellow balls and 14 pink balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is either blue or yellow?

Correct Answer: (a) 8/15  
Solution:P (blue ball) = 7/30
P (yellow ball) = 9/30
Required probability = 7/30 + 9/30 = 8/15