Example A and B play a game in which A’s chance of winning is 2/9. In a series of 8 games, what is the chance that A will win at least 9 games ?

Solution : Here A’s chance of winning = p = 2/9

Therefore q = 1 - p = 1 - 2/9 = 7/9, n = 8

The probability (A will win at least 6 games in a series of 8 games)

Example Assuming half of a population is vegetarian the chance of an individual being a vegetarian is 0.5. Assuming that 100 investigators take a sample of 10 individuals to see whether they are vegetarians, how many investigators do you expect will report that three or less were vegetarian ?

Solution : For one investigator,

p = 0.5 Þ q = 0.5 and n = 10

Then, probability of 3 or less vegetarian is p (x £ 3)

Now p (x £ 3) = p (x = 0) + p (x = 1) + p (x = 2) + p (x = 3)

For 100 investigators we expect 100 ´ p (x £ 3)

= 100 ´ 0.1719

= 17.19 i.e. 17 individuals were vegetarians

Example The incidence of occupational disease in an industry is such that the workmen have 20% chance of suffering from it. What is the probability of 4 or more workmen out of 6 contacting the disease ?

Solution : Here n = 6, p = 0.2 therefore q = 1- 0.2 = 0.8

Probability of out of 6, 4 or more workmen will contact the disease,

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Index

7. 1 Introduction
7. 2 Trial
7. 3 Sample Space
7. 4 Definition of Probability
7. 5 The Laws of Probability
7. 6 Conditional Probability
7. 7 Theoretical Distribution
7. 8 Binomial Distribution
7. 9 Normal Distribution
Chapter 8