7. Conditional Probability

If E1 and E2 are two events, the probability that E2 occurs given that E1 has occurred is denoted by P(E2|E1).

P(E2|E1) is called the conditional probability of E2 given that E1 has occurred.

Calculating Conditional Probability

Let E1 and E2 be any two events defined in a sample space S such that P(E1) > 0.

The conditional probability of E2, assuming E1 has already occurred, is given by

MATH


EXAMPLE 1

Let A denote the event `student is female' and let B denote the event `student is French'. In a class of 100 students suppose 60 are French, and suppose that 10 of the French students are females. Find the probability that if I pick a French student, it will be a girl, that is, find P(A|B).


Answer


EXAMPLE 2

What is the probability that the total of two dice will be greater than 8, given that the first die is a 6?


Answer




Didn't find what you are looking for on this page? Try search:

The IntMath Newsletter

Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!

Given name: * required

Family name:

email: * required

See the Interactive Mathematics spam guarantee.

Probability Lessons on DVD

get MathTutorDVDs

Easy to understand probability lessons on DVD. See samples before you commit.

More info: Probability videos

 

Bookmark this page

Add this page to diigo, Redditt, etc.

 

 


Need a break? Play a math game. Well, they all involve math... No, really!

dumbolf memoTST bola shadow factory mindfields trick-hoops-challenge crystal clear