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What Is a Conditional Probability?

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

P (AB) = P (A B) P (B)

Example 1

In Nick’s class, 50% of the students like sushi, and 30% like both sushi and kebab. 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 (AB). Using the formula above, you get

P (A B) P (B) = 0.3 0.5 = 0.6,

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

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The Chain Rule of Conditional Probabilities