1. A pair of fair dice is rolled. Let E denote the event that the number landing uppermost on the first die is a 3, and let F denote the event that the sum of the numbers landing uppermost is 6. Determine whether E and F are independent events.
3. Copykwik has four photocopy machines: A, B, C and D. The probability that a given machine will break down on a particular day is
P(A) = 1/50, P(B) = 1/60, P(C) = 1/75, P(D) = 1/40 .
Assuming independence, what is the probability on a particular day that
a. All four machines will break down?
b. None of the machines will break down?
Probabilities are clearly explored in this case.