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Example The probability that a man aged 60 will live to be 70 is 0.65. What is the probability that out of 10 men, now 60, at least 7 will live to be 70?

Solution : P = The probability that a man aged 60 will live to be 70 = 65

\ q = 1 - P = 1 - 0.65 = 0.35

Number of men ( n ) = 10

Probability that at least 7 men will live to 70

= P ( 7 or 8 or 9 or 10 )

Example A and B take turns in throwing dice. The first to throw 10 is awarded the prize, show that if A has the first throw, their chance of winning are in the ratio 12 : 11.

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Solution : The combinations of throwing 10 from two dice can be ( 6 + 4 ), ( 4 + 6 ), ( 5 + 5 ).

The number of combination is 3

Total combinations from two dice = 6 ´ 6 = 36

The probability of throwing 10 =

If A is to win, he should throw 10 in either the first, the third, the fifth, ... throws. Their respective probabilities
are P1 Q2 P, Q4P1.....

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