What is the probability that both A and B occur? What is P(A u B) in this case?

Statistics
Tutor: None Selected Time limit: 1 Day

If we know that event B occurs, the probability of A occurring is 0.5

Oct 8th, 2015

Hello!

By definition, the probability of A if B occurs,

P(A | B) = P(A and B)/P(B).

So if P(A | B) = 0.5, then

P(A and B) = 0.5*P(B).

Also, P(A u B), the same as P(A or B) is equal to

P(A) + P(B) - P(A and B) = P(A) + P(B) - 0.5*P(B) = P(A) + 0.5*P(B).

Please ask if something is unclear.
Oct 8th, 2015

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