Let B and C be two events such that PB 035 and Pc 005 a D

Let B and C be two events such that P(B) = 0.35 and P(c) = 0.05 . (a) Determine P (B U C) , given that B and C are independent. (b) Determine P (B U C) , given that B and C are mutually exclusive. Do not round your responses. (If necessary, consult a list of formulas.)

Solution

a) When B & C are independent P( B n C) = P(B)*P(C)

P(B U C) = P(B) + P(B) -P(B)*P(C) = 0.35+0.05-0.35*0.05 = 0.3825

b)

When B & C are mutually exclusive,P( B n C) = 0

P(B U C) = P(B) + P(B) = 0.35+0.05 = 0.40