Lunch Meeting Probability for two person to meet in given 1 hour slot and none would wait more then 15 minute. [closed]

probability

Per @AppDeveloper's request changing it from a comment to an answer:

Just and idea: consider $0$ to $30$ min, the other half is the same by symmetry.

If A arrives at $0$ min, B has to arrive between $0$ and $15$ min, i.e., $p(B\leq 15|A=0)=\frac{1}{4}$.

If A arrives after $15$ min, $p(B|A)=\frac{1}{2}$.

Applying conditional probabilities and integrating, get for $t \geq 15$ min $p(B|A)p(A)=\frac{1}{8}$ and for $0 \leq t \leq 15$, $p(B|A)p(A)=\frac{3}{32}$ Adding together and multiplying by $2$, get $\frac{7}{16}$.


Ah I am surprised the geometric solution has not come up yet. Think of the total times as a square in the coordinate plane, so that each time frame will be 15 mins. The graph will be something like a strip up the diagonal, whose area is very easy to calculate: enter image description here

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