Hannah coaches a youth soccer team here in Bowling Green. Tomorrow night they ha

Question

Hannah coaches a youth soccer team here in Bowling Green. Tomorrow night they have a game. Suppose there is a 45% chance that her team will lose. Regardless of whether or not her team loses, Hannah figures there is a 60% chance that a parent will complain about something to her after the game. From previous seasons, Hannah knows that the probability that her team loses and a parent complains is 35%. Let L = the event that her team loses and C = the event that a parent complains.

Suppose Hannah's soccer team loses. What is the probability that a parent complains? Round to 2 decimals.

If a parent complains, what is the probability that Hannah's team loses? Round to 2 decimals.

What is the probability that Hannah's team wins tomorrow night? Round to two decimals.

Suppose Hannah's soccer team loses. What is the probability that a parent does not complain? Round to 2 decimals.

Explanation / Answer

P(L) = 0.45

P(C ) = 0.60

P(L and C) = 0.35

.

P(C | L) = Probability that parent complains given that the team loses

This is the conditional probability , and its formula is as follows:

P(C | L) = P(C and L) / P(L)

P(C | L) = 0.35 / 0.45

P(C | L) = 0.7778

.

P(L | C) = Probability that the team loses , given that the parent complains

P(L | C) = P(L and C) / P(C )

P( L | C) = 0.35 / 0.60

P( L | C) = 0.5833

.

Probability that Hannah's team wins = 1 - P(L)

P(W) = 1 - 0.45 = 0.55

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