Question

The coach of a summer soccer team has observed that his team has a 55% chance of winning games played on rainy days and a 60% chance of winning games on days its not raining. The weather forecast predicts there is a 75% chance of rain (see details)?

The coach of a summer soccer team has observed that his team has a 55% chance of winning games played on rainy days and a 60% chance of winning games on days its not raining. The weather forecast predicts there is a 75% chance of rain tomorrow. If the the team has a game, what is the probability that they will win?

Answer 1

The probability that they will win is `0.5625`

Explanation:

If there are two outcomes say `X_1` and `X_2`, then

`E(X_1+X_2)=E(X_1)+E(X_2)`

Let `X_1` be the outcome that it rains and they win. The probability is `75/100xx55/100=0.4125`

and `X_2` be the outcome that it does not rain and they win. The probability is `25/100xx60/100=0.15`

Hence, the probability that they will win is `0.4125+0.15=0.5625`