Friends Complete

What is the probability that the two friends meet? The issue is complete in detail box.box?

Two friends, Candy Cane and Ann are Archy shopping at the mall. They agree to separate for a while and then meet for lunch. They plan to meet in front of Harold Square Store clothing between 12:00 and 1:00 P M. He who arrives first agrees to wait 15 minutes for other arrived. After 15 minutes, this person will leave and continue shopping. What is the likelihood that they will meet if each girl arrives at any time between 12:00 and 13:00?

A = Ann, C = Candy Suppose that A arrives at time t minutes after 12 problems they face is: P1 + P2, where P1 C = prob arrived some time in the last 15 minutes, and C = P2 problems will arrive shortly in the next 15 minutes. P1 and P2 can be more easily determined graphically. First we will draw P1 P1 cons clearly t, for t> or = 15, then P1 = 15 min / 60 min = 1 / 4, that C had a "window" full 15 minutes to arrive, but for t <15, C had only a "window" of length t minutes to arrive, P1 = min rpm = 60 t/60 As t varies from 0 to 15, P1 will increase linearly from 0 to 1 / 4 Thus, the graph P1 cons t, for t ranging from 0 to 60 At time t = 0, P1 = 0 P1 then increases so linear up to t = 15, P1 = 1 / 4 t = 15 at t = 60, P1 maintains a constant value of 1 / 4 of the P1 This chart is fairly simple, and you must take forward the next step. Like all moments between t = 0 and t = 60 are equally likely (ie A arrives at any time between 12 and 1), then average value of P1 for all values ​​of t will be equal to the area under the curve, divided by 60. This area is ((1 / 2 * 15 * 1 / 4) + (45 * 1 / 4)) / 60 which is as follows: mean value of P1 = 105 / 480 = P1 P2, due to symmetry P1 is C prob gets there first, and they meet P2 is a problem arrives first, and they meet. And there is no reason that these 2 probs would be different. So they meet Prob = 2 * 105 / 480 = 0.4375

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