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Chapter 6: Q.6.13 (page 271)

A man and a woman agree to meet at a certain location about 12:30 p.m. If the man arrives at a time uniformly distributed between 12:15 and 12:45, and if the woman independently arrives at a time uniformly distributed between 12:00 and 1 p.m., find the probability that the first to arrive waits no longer than 5 minutes. What is the probability that the man arrives first?

Short Answer

Expert verified

The probability that the first to arrive wants no longer that 5 minute is 0.1667

And the probability that man arrives first is0.5


Step by step solution

01

Content Introduction

The probability that the first to arrive waits no longer than 5 minutes. also probability that the first to arrive .

02

Probability of arrival within 5 minutes

P(|X-Y|鈮�5)=P(X-5<Y<X+5)=P(x-5<Y<x+5)=鈭�-鈭�鈭�鈭�x-5蟺+5fX,Y(x,y)dydx=鈭�15x-545鈭�18001511800dydx=11800鈭�1545(y)x-5x+5dx=11800鈭�154510dx=11800脳10脳(x)1545

=11800脳10脳30=16鈮�0.1667

Therefore, the probability that the first to arrive wants no longer that 5 minute is 0.1667

03

Compute probability that man arrives first.

P(X<Y)=P(x<Y)=鈭�-鈭�鈭�鈭�xfx,y(x,y)dydx=鈭�1545鈭�x6011800dydx=11800鈭�1545(y)x60dx=11800鈭�i545(60-x)dx=11800脳60x-x221545=11800脳900=12

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