Paper 4: Fundamentals of Business Mathematics & Statistic

9.10 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Probability

When events are dependent :

If the events are dependent, the probability is conditional. Two events A and B are dependent ; B occurs

only when A is known to have occurred.

P (B|A) means the probability of B given that A has occurred.

P(B|A) P(AB) A; P P AB( )

P(A) B P(B)

=^ =

(^)
Example 13 :
A man want to marry a girl having qualities: White complexion the probability of getting such girl is 1 in 20.
Handsome dowry - the probabihty of getting is 1 in 50. Westernised style - the probability is 1 in 100.
Find out the probability of his getting married to such a girl, who has all the three qualities.
Solution:
The probability of a girl with white complexion= 201 or 0.05. The probability of a girl with handsome dowry
1
= 50 or 0.02. The probabihty of a girl with westernised style

1

= 100 or 0.01. Since the events are

independent, the probabihty of simultaneous occurrence of all three qualities =

1 1 1 0.05 0.02 0.01 0.00001

20 50 100× × = × × =

Example 14 :

A university has to select an examiner from a list of 50 persons, 20 of them women and 30 men, 10 of them

knowing Hindi and 40 not. 15 of them being teachers and the remaining 35 not. What is the probability of

the University selecting a Hindi-knowing women teacher?

Solution:

Probability of selecting a women =^2050

Probability of selecting a teacher =^1550

Probability of selecting a Hindi-knowing candidate =^1050

Since the events are independent the probabihty of the University selecting a Hindi-knowing woman teacher

is :

2 0 1 5 1 0 3

5 0 5 0 5 0 1 2 5× × = or 0.024.

Example 15 :

A ball is drawn at random from a box containing 6 red balls, 4 white balls and 5 blue balls. Determine the

probability that it is :

(i) Red (ii) white, (iii) Blue, (iv) Not Red and (v) Red or White.