Question

Assume Pr[A U B]=.75 and Pr[A]=.3 What is Pr[B] if A and B are independent?

Answer 1

Pr(A U B) = Pr(A) + Pr(B) - Pr(A intersect B)
A and B are independent, so what does the above equation simplify to? From there, you should have your answer.

Answer 2

Is A intersection B just Pr[A]?

Answer 3

Close, but not quite. A intersect B are the elements that are in A that are also in B. But, the two sets are independent, which means there is no element which is in both. I can draw a picture if you'd like.

Answer 4

If they are disjoint, then Pr(A intersect B)=0 and Pr(B)=Pr(A U B)-Pr(A)=.45, but it keeps saying that is wrong and that is only if they are disjoint, not independent

Answer 5

You're right, sorry. I'm mistaken. I only took one probability course as an undergraduate.

Pr(A intersect B) = Pr(A)*Pr(B) if A and B are independent.

Answer 6

I'm not sure how I would find B from what I have though

Answer 7

P(A U B) = P(A) + P(B) - P(A intersect B) = P(A) + P(B) - P(A)*P(B)

So, 0.75 = 0.3 + P(B) - 0.3*P(B)
=> 0.45 = 0.7P(B)
P(B) = 0.6428 (rounded)

Answer 8

Thank you so much!!!

Answer 9

You're welcome. Sorry for the confusion.

Answer 10

No worries!