Suppose that two machines 1 and 2 in a factory are operated independently of each other.

Question

Suppose that two machines 1 and 2 in a factory are operated independently of each other. Let AA be the event that machine 1 will become inoperative during a given 8-hour period; let BB be the event that machine 2 will become inoperative during the same period; and suppose that P(A)=1/3 and P(B)=1/6. What is the probability that at least one of the machines will become inoperative during the given period? Answer exactly.

Answer 1

To find the probability of "at least one" it is often easier to do 1 - the complement,

so, 1 - P(neither become inoperative) = 1 - (2/3 * 5/6) = 1 - 5/9 = 4/9