1. a. P(A  B) = 0.7

b. P(A I B) = 0.5

c. They are independent events as P(A I B) = P(A) or P(AB) = P(A) x P(B)

2. a. P(A  B) = 0.1

b. P(B) = 0.2

3. a. P(B) = 0.3

b. P(A  B) = 0.65

c. The events cannot be mutually exclusive as P(A  B) = 0.15 ≠ 0

4.

 

a. P(black cube) = 0.25

b. P(black marble) = 0.15

c. P (red I cube) = 0.333 (to 3 d.p.)