Questionuser of media?
83. First serve Tennis great Andy Murray made $60 \%$ of his pg 342 first serves in a recent season. When Murray made his first serve, he won $76 \%$ of the points. When Murray missed his first serve and had to serve again, he won only $54 \%$ of the points. ${ }^{21}$ Suppose you randomly choose a point on which Murray served. You get distracted before seeing his first serve but look up in time to see Murray win the point. What's the probability that he missed his first serve?

Studdy Solution
Use Bayes' Theorem to find the probability that Murray missed his first serve given that he won the point:
$P(\text{First Serve Missed} | \text{Win}) = \frac{P(\text{Win} | \text{First Serve Missed}) \cdot P(\text{First Serve Missed})}{P(\text{Win})}$
$P(\text{First Serve Missed} | \text{Win}) = \frac{0.54 \times 0.40}{0.672}$
$P(\text{First Serve Missed} | \text{Win}) = \frac{0.216}{0.672} \approx 0.3214$
The probability that Andy Murray missed his first serve given that he won the point is approximately:
$$\boxed{0.3214}$$