In a certain state, 25% of all cars emit excessive amount of pollutants. If the
probability is 0.99 that a car emitting excessive amount of pollutants will fail the
state’s vehicular emission test, and the probability is 0.17 that a car not emitting
excessive amount of pollutants will nevertheless fail the test, what is the probability
that a car which fails the test actually emits excessive amount of pollutants?
One baseball team won only 41% of their games in the 2010 season. Assuming that
this team has a 41% chance of winning each game next season, what is the probability
that this team can win exactly 15 games in the first 20 games of the 2011 season?
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