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counting and probability senior
Problem
Alice and Bob each arrive at a party at a random time between 1:00 and 2:00. If Alice arrives after Bob, what is the probability that Bob arrived before 1:30?
Solution
We let the -axis represent the time Bob arrives, and the -axis represent the time Alice arrives. Then we shade in the region where Alice arrives after Bob, and mark off the part of that area where Bob arrives before 1:30.
We need the ratio of the area of the shaded region to the left of the line marking 1:30 to the area of the whole shaded region. This ratio is .
We need the ratio of the area of the shaded region to the left of the line marking 1:30 to the area of the whole shaded region. This ratio is .
Final answer
\frac{3}{4}