Paper 4: Fundamentals of Business Mathematics & Statistic

9.12 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Probability

This is known as Bayes’ Theorem.

The following example illustrate the application of Baye’s Theorem.

The above calculation can be verified as follows :

If 1,000 scooters were produced by the two plants in a particular week, the number of scooters produced

by Plant I & Plant II are respectively:

l,000 x 80% = 800 scooters

1,000 x 20% = 200 scooters

The number of standard quality scooters produced by Plant I :

800 x 85/100 = 680 scooters

The number of standard quality scooters produced by Plant II :

200 x 65/100 = 130 Scooters.

The probability that a standard quality scooter was produced by Plant I is :

680 680 68

=680 130 810 81+ = =

The probability that a standard quality scooter was produced by Plant II is :

130 130 13

=680 130 810 81+ = =

The same process i.e. revision can be repeated if more information is made available. Thus it is a good

theorem in improving the quality of probability in decision making under uncertainty.

Example 16 :

You note that your officer is happy on 60% of your calls, so you assign a probability of his being happy on

your visit as 0.6 or 6/10. You have noticed also that if he is happy, he accedes to your request with a

probability of 0.4 or 4/10 whereas if he is not happy, he acedes to the request with a probability of 0.1 or D

or 101. You call one day, and he accedes to your request. What is the probability of his being happy?

Solution :

Let- H be the Hypothesis that the officer is happy and H the Hypothesis that the officer is not happy

P(H)^6

= 10

P(H)^4

= 10

Let A be the event that he accedes to request

P(A /H)^4 , P(A/H)^1

= 10 = 10

To find P(H/A), according to Baye’s Theorem,

P(H) P( )A^64

P(H/ A) H 10 10

P(H) P( ) P(H) PA A 6 4 4 1..

H H 10 10 10 10

× ×

= =

× + × +