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

Question

Hannah coaches a youth soccer team in Bowling Green. Tomorrow night, they have a game. Suppose there is a 36% chance that her team will lose. Regardless of whether her team loses, Hannah figures there is a 59% 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)

Suppose Hannah’s soccer team loses. What is the probability that a parent complains?

If a parent complains after the game, what is the probability that Hannah’s team lost?

What is the probability that Hannah’s team will win tomorrow night?

Suppose Hannah’s soccer team loses. What is the probability that a parent does not complain?

Explanation / Answer

here probabilty of losing  =P(L)=0.36

and winning P(W)=1-0.36=0.64

probability of complaint P(C)=0.59

and probability of no complaint =P(NC)=1-0.59=0.41

probabilty of losing and parent complaing =P(C &L) =0.35

hence probabilty of Winning and parent complaing =P(C &W)=P(C)-P(C &L)=0.59-0.35=0.24

also probability of winning and parent not complaing=P(W & NC) =P(W)-P(W &C)=0.64-0.24=0.40

and  probability of losing and parent not complaing P(L &NC)=P(NC)-P(W &NC)=0.41-0.40=0.01

hence

probability that a parent complains, given Hannal team loses=P(C|L)=0.35/0.36=0.97222

probability that Hannah’s team lost, given parent complains after the game=P(L|C)=0.35/0.59=0.59322

probability that Hannah’s team will win tomorrow night=P(W)=0.64

probability that a parent does not complain,given Hannah’s soccer team loses=P(NC|L)=0.01/0.36=0.02778

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