The multiplication rule of probability

Let A and B be two events. The probability of their intersection is

Also

Example:

Suppose that seven nondefective and three defective goods have been mixed up. To find defective goods, we test them one by one, at random, and without replacement. What is the probability that we are lucky and find both of the defective goods in the first two tests?

Solution:

Let and be the events of finding defective goods in the first and second tests respectively. We are interested in

As we know, there are three defective goods in total 10 goods. Consequently, the probability of selecting a defective good at the first selection is . To calculate the probability , we know that the first good is defective because has already occurred. Because the selections are made without replacement, there are 9 total goods and 2 of them are defective at the time of the second selection. Therefore =2/9. Hence the required probability is

= .

Remark: Multiplication rule can be generalized for calculating the probability of the joint occurrence of several events.

For example, if ,then

Дата добавления: 2015-08-05