problem 11

Using the odds form of Baye’s Theorem,

\frac{P (A | W)}{P (A^{c} | W)} = \frac{P (A)}{P (A^{c})} \frac{P (W | A)}{P (W | A^{c})}

\frac{0.6}{0.4} = \frac{P (A)}{P (A^{c})} \frac{0.7}{0.3}

\frac{P (A)}{P (A^{c})} = 0.643

P (A) = 0.39