I don't understand how to solve this: Suppose P(E) = 49⁄100 , P(Fc ) = 31⁄100 , and P(F ∩ Ec ) = 7⁄20. Find P(E ∪ F).

Answer 1

P(Ec) = 1 - P(E) = 1 - 49/100 = 51/100

P(Ec) = P(F Ec) + P(Fc Ec), so P(Fc Ec) = 51/100 - 7/20 = 16/100 = 4/25

P(E U F) = 1 - P(Fc Ec) = 1 - 4/25 = 21/25