It is known that Party A and Party B are good friends. They agree to meet at the gate of Shanghai park from 9:00 to 10:00 one day. If one of them waits for 20 minutes within the agreed time and does not see the other, they will leave. If both of them fulfill their promise, what is the probability of the two good friends meeting?

It is known that Party A and Party B are good friends. They agree to meet at the gate of Shanghai park from 9:00 to 10:00 one day. If one of them waits for 20 minutes within the agreed time and does not see the other, they will leave. If both of them fulfill their promise, what is the probability of the two good friends meeting?

From the meaning of the question, we know that this question is a geometric probability type. All the events included in the experiment are Ω = {(x, y) | 2 ＜ x ＜ 3, 2 ＜ y ＜ 3}. The area of the set corresponding to the event is s = 1. The event satisfying the condition is a = {(x, y) | 7 ＜ x ＜ 8, 7 ＜ y ＜ 8, and | X-Y ＜ 13. The area of the set corresponding to the event is 1-2 × 12 × 23 × 23 = 59. According to the probability formula of geometric probability type, we get p = 59, so it's good for you The probability of meeting friends is 59