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Two brothers are in a hurry to raise money for an activity. Theamount ofmoney each of...

Two brothers are in a hurry to raise money for an activity. Theamount ofmoney each of them collects is independent of that of the other and is uniformly distributed between $10 and $25. What is the probability that either brother is able to bringhomemore than twice as much money than the other?

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Answer #1

As the two variables X and Y which are the money brought by them are independent of each other, therefore the joint PDF for the amount of money brought by them is modelled here as:

Now the probability that either brother is able to bringhomemore than twice as much money than the other is computed here as:

.

As Y > 2X, the max value of X can only be 12.5 here, because 2*12.5 = 25.

Therefore 1/18 = 0.0556 is the required probability here.

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