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
