The results of students borrowing supplies from the library is summarized as follows: 𝑃(𝐵) = .4 , 𝑃(𝐷) = .3 , 𝑃(𝐷|𝐵) = .5

Question

Let B= student took out a book and let D=student took out a DVD

Calculate:

(a) 𝑃(𝐵′)

(b) 𝑃(𝐵 𝑎𝑛𝑑 𝐷)

(c) 𝑃(𝐵|𝐷)

(d) 𝑃(𝐷 𝑎𝑛𝑑 𝐵′)

Answer 1

a) P(B') = 1 - P(B) = 1 - 0.4 = 0.6

b) P(B and D) = P(B) * P(D|B) = 0.4 * 0.5 = 0.2

c) P(B|D) = P(B and D)/P(D) = 0.2/0.3 = 0.67

d) P(D) = P(D and B) + P(D and B')

P(D and B') = P(D) - P(D and B) = 0.3 - 0.2 = 0.1