To solve the classic "meeting probability" problem (assuming the standard setup where two people meet within a 15-minute window over a 60-minute period), follow these steps:

Step 1: Model the problem

Let (X) and (Y) be the arrival times of the two people, uniformly distributed over ([0,60]) minutes. We need (P(|X-Y| \leq 15)).

Step 2: Calculate the total area

The sample space is a square of side 60:
Total area = (60 \times 60 = 3600).

Step 3: Calculate the non-meeting area

The regions where they don’t meet are two right triangles, each with base and height = (60 - 15 = 45) minutes.
Area of one triangle = (\frac{1}{2} \times 45 \times 45 = 1012.5).
Total non-meeting area = (2 \times 1012.5 = 2025).

Step 4: Compute the meeting probability

Meeting area = Total area - Non-meeting area = (3600 - 2025 = 1575).
Probability = (\frac{1575}{3600} = \frac{7}{16}).

Answer: (\boxed{\dfrac{7}{16}})

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