"A first Course in probability"-chaper3-conditional probability and independence-basic formula

EX1:

Joey 80% sure he put the missing key in one of the two pockets of his coat. He was 40% sure to put it in the left pocket and 40% OK in the right pocket. If you check the left pocket and find that the key is not found, then what is the condition probability of the key in the right pocket?

Analysis: Very basic conditional probability of the problem, the key to solve is to find out which event is the event we want to solve the condition of the event.

To solve the conditional probability problem, it is not necessary to apply its definition, and the conditional probability can be obtained intuitively and simply by generating the sample subspace of the conditional event, if the sample point of the sample space is possible. Here are a few examples to illustrate.

EX2:

Toss a coin two times, assuming that the sample space s={(H,h), (h,t), (T,h), (t,t)}4 sample points are likely to occur, in order to give the following event after the two coins are facing up the conditional probability:

(a) The first one is facing upwards.

(b) At least one upward.

Analysis: Due to assumptions, we can easily find the sample subspace of a conditional event.

Based on the original definition of conditional probabilities, we can easily get the following formula:

The formula can be generalized to get the following multiplication rules:

"A first Course in probability"-chaper3-conditional probability and independence-basic formula