Rules of Probability

Question

Let S = {a, b, c, d, e, f} with P(b) = 0.11, P(c) = 0.18, P(d) = 0.23, P(e) = 0.19, and P(f) = 0.16. Let E = {c, d, e} and F = {a, b, d, e}. Find P(a), P(E), and P(F).

P(a)

P(E)

P(F)

I found P(E). Can't seem to figure it out. Any help is appreciated thanks.

Answer 1

P(a) = 1 - 0.11 - 0.18 - 0.23 - 0.19 - 0.16 = 0.13

P(E) = P(c) + P(d) + P(e) = 0.18 + 0.23 + 0.19 = 0.6

P(F) = P(a) + P(b) + P(d) + P(e) = 0.13 + 0.11 + 0.23 + 0.19 = 0.66