Question

7	My wife will have a birthday next Thursday and sometimes I forget to get her a birthday present. If I forget to get her a present, she may or may not get mad at me. Of course, she may get mad at me even if I do buy her a present. Let A = event that I remember to buy her a present and B = event that she gets mad at me. These events are obviously not independent and not mutually exclusive. Calculate the probability that i remember to buy a present OR she gets mad at me: P(A + B). Values for P(A), P(B), P(A/B), and P(B/A) are shown on the right.							P(A) =	0.625
								P(B) =	0.575
								P(A/B) =	0.696
								P(B/A) =	0.640
		a	0.800	-1.5179
		b	0.841	-0.118
		c	0.000	-2.7624
		d	0.400	-0.5233
		e	None	0.7958

Answer 1

P(A⋃B) = P(A) + P(B) - P(A⋂B)

It is given that P(A) = 0.625 and P(B) = 0.575.

So first we need to find P(A⋂B)

Based on Baye's theorm, we can say that

P(A⋂B) = P(A)*P(B|A) = 0.625*0.640 = 0.400

P(A⋃B) = P(A) + P(B) - P(A⋂B) = 0.625 + 0.575 - 0.400

P(A⋃B) = 0.800

Thus, Option A is correct