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

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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).

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