Paper 4: Fundamentals of Business Mathematics & Statistic

9.18 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Probability

Example 23 :

A problem in statistics is given to three students A, B, C whose chances of solving it are 1/2, 1/3, 1/4

respectively. What is the probability that the problem will be solved?

Solution:

The probability that A fails to soive the problem = −^1 1 12 2=

The probability that B fails to solve the problem = −^1 3 31 2=

The probability that C fails to solve the problem = −^1 1 34 4=

The probability that the problem is not solved by A, B and C = × ×1 2 3 12 3 4 4=

Therefore, the probability that the problem is solved = − =^1 1 34 4

Example 24 :

An ordinary die is tossed twice and the difference between the number of spots turned up is noted. Find the

probability of a difference of 3.

Solution :

The sample space consists of 36 values.

The event space has the following 6 cases : (1, 4), (2, 5), (3, 6), (4, 1), (5, 2), (6, 3)

The required probability = 366

Example 25 :

From a pack of 52 cards, two cards are drawn at random ; find the chance that one is a knave and the

other a queen.

Solution :

Sample space =^52 C 2

Event space =^4 C 1 x^4 C 1

(as there are 4 queens and 4 knaves in the pack)

Required Probability =

(^4141)
(^522)

C C 8

C^663

= × =

Example 26 :

A bag contains 7 red balls and 5 white balls. 4 balls are drawn at random. What is the probability that (i) all

of them are red ; (ii) two of them are red and two white?