Conditional probability

Definition:

Conditional probability is the probability that an event will occur given that another event has already occurred. If A and B are two events, then the conditional probability of A is written as and read as “the probability of A given that B has already occurred”.

If A and B are two events, then

and

given that and .

Example:

A box contains black chips and white chips. A person selects two chips without replacement. If the probability of selecting a black chip and a white chip is 15/56, and the probability of selecting a black chip on the first draw is 3/8, find the probability of selecting the white chip on the second draw, given that the first chip selected was a black chip.

Solution:

Let B =selecting a black chip

W =selecting a white chip.

Then .

Hence, the probability of selecting a white chip on the second draw given that the first chip selected was black is 5/7.

Example:

In a certain region of Kazakhstan, the probability that a person lives at least 80 years is 0.75 and the probability that he or she lives at least 90 years is 0.63. What is the probability that randomly selected 80-year old person from this region will survive to become 90?

Solution:

Let A and B be the events that the person selected survives to become 90

and 80 years old, respectively. We are interested in . By definition,

(Note that in this case ).

Дата добавления: 2015-08-05