Thanks to a generous and eccentric donor, 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 none of the fax machines need toner?
A)1.1500
B)1.1658
C).8578
D).7696

Question

Quizplus · Accepted Answer

Let's assume that the three fax machines are independent of each other and that each of them has a probability of 0.2 (1/5) of needing a toner replacement in a 1-hour period.

The probability that none of them will need toner in a given 1-hour period is:

P(no toner needed) = (0.8)³ = 0.512

Since the secretary takes 15 minutes (0.25 hours) to replace the toner, the probability that none of the fax machines will need toner in the next 15 minutes is:

P(no toner needed in 15 min) = (0.512)³ = 0.134

Therefore, the probability that none of the fax machines will need toner in the next 15 minutes is 0.8578 (1 - 0.134).

Thanks to a Generous and Eccentric Donor, the School of Business