Question

A student goes to the library. Let events B = the student checks out a book and D = the student check out a DVD. Suppose that P(B) = 0.40, P(D) = 0.30 and P(D|B) = 0.5.

a. Find P(B AND D).

b. Find P(B OR D).

Short answer

P(B AND D) = 0.20

P(B OR D) = 0.50

Step-by-step solution

Basic Concepts & Formulas 

• Pr (student checks DVD, given he checks Book) = P(D|B) =

Pr (He checks both Book & DVD) / Pr (He checks Book) = P (D ∩ B) / P (B)

• Pr (Student checks Book or DVD) = P(B OR D) = P (B U D) =

Pr (he checks book) + Pr (he checks DVD) + Pr (he checks both) = P(B) + P(D) - P (D∩ B)

Numerical Solution

A] 0.5 = P (D ∩ B) / 0.40

P (D & B) = 0.20

B] P (B U D) = 0.40 + 0.30 - 0.20

B (B or D) = 0.50