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Hannah coaches a youth soccer team in Bowling Green. Tomorrow night, they have a game. Suppose there is a 43% chance that her team will lose. Regardless of whether her team loses, Hannah figures there is a 58% 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.)Suppose Hannah's soccer team loses. What is the probability that a parent complains?

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Answer:

81.40%

Step-by-step explanation:

Probability of losing the game P(L) = 43%

Probability of a parent complaining P(C) = 58%

Probability of losing and a parent complaining P(L and C) = 35%

The probability of a parent complaining given that the team loses is:

[tex]P(C|L) = \frac{P(L\ and\ C)} {P(L)} = \frac{0.35}{0.43}\\ P(C|L) = 0.8140\ or\ 81.40\%[/tex]

If her team loses, the probability that a parent complains is 81.40%

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