Question

The Westerburg High School Soccer Team performs differently in the rain than they do when it doesn't rain. When it rains they have a 80% chance of winning, but when it doesn't rain they have a 50% chance of winning. Given that there is a 20% chance of rain today, what is the probability that they lose their game?

Answer 1

44%

Explanation:

It is given that when it rains they have a 80% chance of winning, but when it doesn't rain they have a 50% chance of winning.

P(Rains-winning) = 0.8

P(Rains-losing) = 1 - 0.8 = 0.2

P(Doesn't Rains- winning) = 0.5

P(Doesn't Rains-losing) = 1 - 0.5 = 0.5

Given that there is a 20% chance of rain today. We need to find the probability that they lose their game.

P(Rain) = 0.2

P(No Rain) = 1 - 0.2 = 0.8

The probability that there is rain and they loss is:

`0.2* 0.2=0.04`

The probability that there is no rain and they loss is:

`0.8* 0.5=0.4`

The probability that they lose their game is

`Probability=0.04+0.4=0.44`

Therefore, the probability that they lose their game is 44%.

Answer 2

There are two scenarios under which the team loses.
Either it rains and they lose, which has probability 20% * 20% = 4%. Or it doesn't rain and they lose, which has probability 80% * 50% = 40%.
Adding these two probabilities gives us 44%, so the correct answer is C.