Probability problems

Question

Q: if A and B are two events in S and P(A)=2/3 and P(B)=1/4 and P(A' intersection B')=1/6

1) P(A' - B') =

a) 1/6

b)1/3

c)3/6

d)11/15

__________________________

2) P( A U B ) =

a) 1/3

b) 2/6

c) 5/6

d) 2/12

____________________________

3) P(A intersection B) =

a) 1/3

b) 2/5

c)0

d) 1/12

I need the answer to these Qs

Answer 1

If you draw a Venn diagram, you can see that:

A' - B' = not A and B = B - (A intersection B)

A' intersection B' = not A and not B = (A U B)'

So, P(A' intersection B') = P( (A U B)' ) = 1 - P(A U B)

1/6 = 1 - P(A U B)

P(A U B) = 5/6

Next, P(A U B) = P(A) + P(B) - P(A intersection B)

P(A intersection B) = P(A) + P(B) - P(A U B) = 2/3 + 1/4 - 5/6 = 1/12

Finally, P(A' - B') = P(B - (A intersection B)) = P(B) - P(A intersection B) = 1/4 - 1/12 = 1/6