Another GRE study question
Let A, B, C, and D be events for which P(A or B) = 0.6, P(A) = 0.2,
P(C or D) = 0.6,and P(C) = 0.5. The events A and B are mutually
exclusive, and the events C and D are independent.
Part (a) asks find P(B), which is
$P(A \cup B) = P(A) + P(B)$
$0.6 = 0.2 + P(B)$
$P(B) = 0.4$
But part (b) asks find P(D), and when I try, my answer is $0.1$
$P(D) = P(C\cup D) – P(C) = 0.6 – 0.5 = 0.1$
This is incorrect. According to the study guide, answer is $0.2$
Please explain
Best Answer
$$P(C\cup D) = P(C)+P(D)-P(C\cap D)$$
$$0.6 = 0.5 +P(D) - P(C).P(D) = 0.5 +P(D) - 0.5P(D)$$
$$.5P(D) = .1 $$
$$P(D) = .2$$
The catch is Cand D are independent, then $P(C\cap D$ = P(C).P(D)