Question

Your favorite team is in the World Series. You have assigned a probability of 63% that they will win the championship. Past records indicate that when teams win the championship, they win the first game of the series 72% of the time. When they lose the championship, they win the first game 27% of the time. The first game is over and your team has lost. What is the probability that they will win the World Series?

Answer 1

Answer:

0.3950

Step-by-step explanation:

Any team team will win the championship with probability 63% that is

P(W)=0.63

when teams win the championship, they win the first game of the series 72% of the time that is

P(F|W)=0.72

When they lose the championship, they win the first game 27% of the time.

P(F|W')=0.27

The probability that they will win the World Series when the first game is over and your team has lost that is

P(W|F')

Now, By Bayes theorem

$\begin{array}{l}P\left(W | F^{\prime}\right)=\frac{P\left(F^{\prime} | W\right) P(W)}{P\left(F^{\prime} | W\right) P(W)+P\left(F^{\prime} | W^{\prime}\right) P\left(W^{\prime}\right)} \\\quad=\frac{[1-P(F | W)] P(W)}{[1-P(F | W)] P(W)+\left[1-P\left(F | W^{\prime}\right)\right][1-P(W)]} \\\quad=\frac{[1-0.72] \times 0.63}{[1-0.72] \times 0.63+[1-0.27][1-0.63]} \\\quad=\frac{0.28\times 0.63}{0.28\times 0.63+0.73 \times 0.37} \\=0.3950\end{array}$