Answer
= $\frac{21}{29}$ $\approx$ 0.7241
Work Step by Step
Let E = success is predicted.
F = Success
P(F) =60% = 0.6
P(E|F) = 70% = 0.7
P(E|~F) = 60% = 0.4
Use the complement rule
P(~F) = 1- P(F) = 1-0.6= 0.4
Use Bayes Therorem
P(F|E)=$\frac{0.7\times0.6}{(0.7\times0.6)+(0.4\times0.4)}$
= $\frac{21}{29}$ $\approx$ 0.7241
