Conditional Probability & Independence

Question

Let C and D be independent events with P(C) = .2 and P(D) = .3.

(a) Find P(C ᴜ D).

(b) Find P(C ∩ D).

Answer 1

When two events, A and B, are independent, means An event that is not effected by other events.

P(A and B) = P(A) · P(B)

(a) P(C U D) = P(C) + P(D) - P(C ∩ D).=> P(C) + P(D) - P(C) * P(D) = 0.2+ 0.3 - (0.2 * 0.3) = 0.44

(b) P(C ∩ D) = P(C) * P(D) = 0.2 * 0.3 = 0.06

Hope this helps! for any further doubts i am available to clarify!