Hannah coaches a youth soccer team in Philadelphia. Tomorrow night, they have a

Question

Hannah coaches a youth soccer team in Philadelphia. Tomorrow night, they have a game. Suppose there is a 45% chance that her team will lose. Regardless of whether her team loses, Hannah figures there is a 50% 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%.  (Hint: Organize and label the given information first before starting. Write out the probability statement for each question before calculating anything.)

(Round all probabilities to four decimals)

Explanation / Answer

P(lose) = 0.45, P(parent complain) = 0.5, P(lose and parent complain) = 0.35

a) P(parent complain | team loses) = P(parent complain and team loses)/P(team loses) = 0.35/0.45 = 0.7778

b) P(loses | parent complain) = P(parent complain and team loses)/P(parent complain) = 0.35/0.5 = 0.7

c) P(win) = 1 - P(lose) = 1 - 0.45 = 0.55

d) P(loses | parent does not complains)*P(parent does not complain) + P(loses | parent complains)*P(parent complains) = P(loses), P(loses | parent does not complains) = 0.2

By bayes theorem,
P(parent does not complain | loses) = P(loses | parent does not complain)*P(parent does not complain)/P(loses)
= 0.2 * 0.5/0.45 = 0.2222

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