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?

44%

Step-by-step 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:

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

The probability that they lose their game is

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