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

Question

Quizplus · Accepted Answer

Since each fax machine needs toner after approximately 5 hours of use and there are 3 fax machines, the total time until they all need toner would be approximately 15 hours (5 hours/machine * 3 machines = 15 hours).

In order for 2 fax machines to need toner at the same time, we can think of this as a "success" event, meaning that the first machine needs toner and then the second machine also needs toner before the third machine needs toner.

Using the formula for the probability of independent events occurring together, we can calculate the probability as follows:

P(2 fax machines need toner at same time) = P(first machine needs toner) * P(second machine needs toner before third machine does)

The probability that the first machine needs toner is 1 (since at least one machine needs toner). The probability that the second machine needs toner before the third machine does can be calculated as follows:

P(second machine needs toner before third machine does) = P(second machine needs toner) * P(third machine doesn't need toner)

To calculate P(second machine needs toner), we can use the fact that each machine operates independently of the others. Therefore, the probability that any one machine needs toner at a given time is 1/3. So, 
P(second machine needs toner) = 1/3

To calculate P(third machine doesn't need toner), we can use the fact that the first two machines have already used up some of the time until all the machines need toner. After the first machine needs toner, there are 10 hours until the next machine needs toner. Therefore, the probability that the third machine doesn't need toner at this point is 10/15 (or 2/3).

Putting it all together, we get:

P(2 fax machines need toner at same time) = 1 * (1/3 * 2/3) = 2/9 = 0.2222...

So, the answer is C), with a probability of 0.0129.

The School of Business Has 3 Fax Machines