Question

Given the following:

P(A) = .72
P(B) = .28
P(A n B) = .14

Find the following:

e) P(A and B^C)
f) P(A^C and B)

I've completed the rest of the problems, but I'm stuck on these two. Help?

Answer 1

Drawing a Venn diagram might help. What does "n" mean? is it "U" for union? ^ for intersection? something else?

Answer 2

Ah, I feel silly. I don't know the proper name for it - it looks like an upside-down U to represent intersection or 'and'.

Answer 3

U means "union" and is A or B or both A and B.

Upside-down U, like n perhaps, means both A and B but not singly "intersection."

To avoid double-counting those at the intersection, the formula for P(A U B) = P(A) + P(B) - P(A^B), where I use ^ to indicate intersection.

The need for minus term becomes clear if you imagine A and B being almost identical, so that if you added P(A) and P(B) you would get almost 2 P(A) or 2 P(B) rather than P(A) or P(B) approximately. Have to correct so as not to double-count intersection.

Assuming n means intersection

P(A) + P(B) = 0.72 + 0.28 - 0.12 =0.88

What is C and how does it interact with A and B in a Venn diagram?