A meteorologist is saying that, sometime in the next 45 minutes, a thunderstorm

Question

A meteorologist is saying that, sometime in the next 45 minutes, a thunderstorm is supposed to start. Lets assume that the start time is distributed uniformly over 0, 45] (a) I need to walk home! But that takes 10 minutes. Whats the probability that its not going to start raining over the next 10 minutes? (b) Now 10 minutes have elapsed, but I'm still here. And it actually hasn't started raining yet, I could have gone home! But maybe I should go now? What's the probability that it's not going to rain in the next 10 minutes?

Explanation / Answer

here above is a uniform distribution for which paramter a=0 and b=45

hence P(X<=x)=(x-a)/(b-a)=x/45

therefore a) P(rain does not start in next 10 minute)=P(X>10)=1-P(X<10)=1-10/45=35/45=7/9

b)

P(X>20|X>10) =P(X>20)/P(X>10)=(1-20/45)/(1-10/45)=25/35=5/7

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