Question

You and your sister go get some ice-cream. Two different servers give you and your sister ice-cream. Server A serves you and pours an amount of sprinkles on top of the scoop that is distributed uniformly between one ounce and three ounces. Server B serves your sister and pours an amount of sprinkles on top of the scoop that is distributed uniformly between half an ounce and two ounces. What is the probability that you get more sprinkles than your sister?

Draw a picture if you can and explain the bounds.

Answer 1

Suppose, random variable X denotes amount of sprinkles I got and random variable Y denotes amount of sprinkles my sister got.

Probability that I get more sprinkles than my sister is given by .

This situation is described in the diagram as follows.

The shaded region (in green) is the region where X>Y.

As the random variables follow uniform distributions independently, required probability can be determined using area as follows.