Question

A student goes to the library. Let events B = the student checks out a book and D = the student checks out a DVD. Suppose that P(B) = 0.40, P(D) = 0.30 and P(B AND D) = 0.20.

a. Find P(B|D).

b. Find P(D|B).

c. Are B and D independent?

d. Are B and D mutually exclusive?

Short answer

a] P(B|D) = 0.66 ; b] P(D|B) = 0.5 ; c] No, B & D are not independent ; D] No, B & D are not mutually exclusive

Step-by-step solution

Probability 

A] P(B|D) = Pr (Student B checks out a book, given he checks out a DVD)

= P (B & D) / P (D) = P (B & D) / P (D) = 0.20 / 0.30 = 0.66

B] P(D|B) = Pr (Student B checks out a DVD, given he checks out a book)

= P (B & D) / P (B) = P (B & D) / P (B) = 0.20 / 0.40 = 0.5

Mutually Exclusiveness & Independence Concepts 

• Mutually Exclusive events are those, which cannot happen simultaneously, like a coin tossed once can't get both head & tail.

As student can check out both a book & a DVD, so event B & D are not mutually exclusive.

• Independent Events are those, whose occurrence of one event doesn't effect occurrence of other event. In case of such events, Pr (A & B) = Pr (A) x Pr (B)

As Pr (B & D) ie looking both book & DVD is not = P (B) P (D) , as 0.40 x 0.30 ≠ 0.20