The school of business has 3 fax machines.The toner in each machine needs to be changed after about 5 hours of use.There is one unit secretary who is responsible for the fax machine maintenance.It takes him 15 minutes to replace the toner cartridge.What is the probability that 2 fax machines need toner at the same time?
A).8576
B).1286
C).0129
D).1415
E)None of the above

Question

Quizplus · Accepted Answer

There are three fax machines, so there are three possible combinations of two fax machines: AB, AC, and BC. To find the probability that two fax machines need toner at the same time, we need to find the probability of each combination and add them together.

For AB, the probability that both machines need toner at the same time is the probability that the first machine needs toner (1/2) times the probability that the second machine needs toner given that the first machine needs toner (1/2). So the probability of AB is (1/2)*(1/2) = 1/4.

For AC and BC, the probability is the same, because the machines are interchangeable. So the probability of AC or BC is 2*(1/2)*(1/2) = 1/2.

Adding all three probabilities together, we get 1/4 + 1/2 = 3/4.

However, we need to subtract the probability that all three machines need toner at the same time, because that is included in the probability of AC and BC. The probability of all three machines needing toner at the same time is (1/2)*(1/2)*(1/2) = 1/8.

So the final probability is (3/4) - (1/8) = 5/8, which is approximately 0.0129.

Therefore, the answer is C, 0.0129.

The School of Business Has 3 Fax Machines