Colorful House of Math logo
Menu iconMenu
Log in

Conditional probability describes events that affect each other. This means that the probability of one event changes if another event has occurred. P(A∣B) is the probability of A occurring given that you “know” that B has already occurred. You can find it with this formula:

P(A∣B)=P(A∩B)P(B)

Example 1

In Nick’s class, 50% of the students like sushi, and 30% like both sushi and kebabs. If you know that Nick likes sushi, what is the probability of him also liking kebab?

Let A be the event “Nick likes kebab”, and let B be the event “Nick likes sushi”. Then you’ll have to find P(A∣B). Using the formula above, you get

P(A∩B)P(B)=0.30.5=0.6,

which tells you that the conditional probability of Nick liking kebab given that he likes sushi is 60 %.

Want to know more?Sign UpIt's free!
White arrow pointing to the LeftPrevious entry
What Are Dependent and Independent Events in Math?
Next entryWhite arrow pointing to the right
The Chain Rule of Conditional Probabilities