Suppose that two integers a and b are uniformly at random selected from S = {-10, -9, …, 9, 10}. Find the probability that max {0, a} = min {0, b}
Try to solve this problem yourself before moving on to the solution below
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Note that a <= 0, as min{0, b} <= 0. Furthermore, we also see that b >= 0, as max{0, a} >= 0. Therefore, we just need to find the probability a <= 0 and b >= 0. There are (21^2 = 441) total ways a and b can be selected. Of those, we have 11 choices for each a and b, as a <= 0 and b >= 0, so our probability is
\( \frac{11^2}{21^2} = \frac{121}{441}.\)
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