Show all workings thanks. An athlete goes for a 2km jog along a straight road. A

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Show all workings thanks.

An athlete goes for a 2km jog along a straight road. At the end, he realizes that he has dropped his keys somewhere along the way and that he was equally likely to have dropped them at any point along the road. (a) What is the probability that the keys are less than 100m away from him? (b) What is the probability that the keys were dropped in the first 500m of the jog? (c) What is the probability that the keys were not dropped in the first 200m and were not dropped in the last 200m?

Explanation / Answer

Question 2

Here as the athelete droped the key in the straight road. so here it is equally probabile to drop it anywhere

so the distribution is uniform distribution. which is

f(x) = 1/2 ; 0 < x < 2

where x is the distance athelete ran from starting point

Here cumulative distribution of the given distribution is

F(X) = x/2 ; 0 < x < 2

(a) so here that means the keys are in between 1.9 km and 2 km

Pr(1.9 km < x < 2 km) = F(2) - F(1.9)

= 2/2 - 1.9/2 = 0.05

(b) Pr(x < 0.5 km) = F(0.5) = 0.5/2 = 0.25

(c) Pr(200 m < x < 1800 m) = Pr(x < 1800 m) - Pr(x < 200 m) = F(1800) - F(200) = 1.8/2 - 0.2/2 = 0.8

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