## Conditional Probability

Conditional probability is the probability of an event occurring given that some other event B has already occurred.

The probability that A occurs, given that B has already occurred is written P(A ) The formula is sometimes written P(A B) = P(A I B) . P(B)

 Example 1 When a die is thrown, an even number occurs. What is the probability that the number is a prime number. Example 2 In any given year the probability of a Japanese car being stolen is 0.012, while for other types it is 0.009. If the proportion of Japanese cars in the country is 0.7, what is the probability that the next car reported stolen is Japanese? P(car is stolen) = P(Japanese stolen) + P(other stolen) = 0.7 x 0.012 + 0.3 x 0.009 = 0.0111 P(Japanese given that it is stolen) = P(Japanese I stolen) Note

The denominator is always the probability of the given event or the event that has already happened.

If the events are independent events then P(A I B) = P(A)

If two events are mutually exclusive events then P(A I B) = 0 and they cannot both happen together