 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2021/discrete-mathematics-continuous-mathematics-and-probability/8/a/iii/solution

Let

R_{1}, R_{2}

P (R_{1} \cap R_{2}) = \frac{m}{N} \frac{m - 1}{N - 1} .

This differs from the product

m^{2} / N^{2}

, since

P (R_{1} \cap R_{2}) - P (R_{1}) P (R_{2}) = - \frac{mn}{N ^{2} ( N - 1 )} < 0.

Thus the events are not independent, for every positive

m, n

 New to topics? Read the docs here!