Two persons A and B agree to meet on 20<sup>th</sup> April 2018 between 6 P.M. and 7 P.M., with the understanding that they will wait no longer than 20 minutes for the other. What is the probability that they meet?
Let A and B arrive x and y minutes after 6 PM, with \(0 \le x, y \le 60\). The sample space is a 60 × 60 square.
They meet if \(|x - y| \le 20\). They don't meet in two corner triangles, each with legs of 40.
Area where they don't meet = \(2 \times \frac{1}{2} \times 40 \times 40 = 1600\).
P(meet) = \(1 - \frac{1600}{3600} = 1 - \frac{4}{9} = \frac{5}{9}\)
Answer: (A) \(\frac{5}{9}\)
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