Example A purse contains 6 silver coins and 3 copper coins. Another purse contains 4 silver coins and 5 copper coins. A purse is selected at random and a coin is drawn from it. What is the probability that it is a silver coin?

Solution :

Let A = the first purse selected

C = a silver coin is drawn from the purse

Since there are two purses
P (A) = and P (B) =

Suppose the event A has occurred. Since there are 6 silver coins out of 9

P (C/A) =

The probability of getting the first purse and a silver coin from it is

P (A Ç C) = P (A) . P (C/ A) =

Similarly, suppose B has occurred then P (C/B) =

P ( B Ç C) = P (B) P (C/ B) =

Now A Ç C and B Ç C are mutually exclusive.

P (A Ç C È B Ç C) = P (A Ç C) + P (B Ç C) =

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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