What is the chance of the school team winning tommorow in the following case:A school baseball team has a 90% chance of winning during a sunny day, and a 50% chance of winning during a cloudy day....

What is the chance of the school team winning tommorow in the following case:

A school baseball team has a 90% chance of winning during a sunny day, and a 50% chance of winning during a cloudy day. They are due to play a game tomorrow against a rival baseball team. The weather forecast says that the chance of a cloudy day is 40 %. What is their chance of winning tomorrow?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A school baseball team has a 90% chance of winning on a sunny day, and a 50% chance of winning on a cloudy day. They are due to play a game against a rival baseball team tomorrow and the weather forecast says that the chance of a cloudy day is 40%.

As there is a 40% probability of the day being cloudy, there is a 60% chance of it being sunny. The probability of the team winning on a cloudy day is 50% and on a sunny day it is 90%. This gives the probability that the team wins tomorrow as 0.4*0.5 + 0.6*0.9 = 0.74

There is a 74% chance that the team wins the game tomorrow.

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