The Readylite Company produces a flashlight which is perfectly reliable except for two components: the battery,which has a random failure rate of one in every five hours of operation; and the light bulb,which has a random failure rate of three in every ten hours.If the company includes both a backup light bulb and a backup battery with each flashlight,what is the probability that the flashlight will perform reliably for one hour (excluding replacement time)?
A)0.6720
B)0.7280
C)0.8736
D)0.9100
E)0.9600

Question

Quizplus · Accepted Answer

To perform reliably for one hour, the flashlight must have both the battery and light bulb functioning throughout the hour. Let us use complementary probability by finding the probability that either the battery or light bulb fails during the hour, and then subtracting that from 1.

The probability of the battery failing during the hour is 1/5. The probability of the light bulb failing during the hour is 3/10. Since these events are independent, we can multiply the probabilities to get the probability of both events occurring, which is:
(1/5) x (3/10) = 3/50

So, the probability of either the battery or light bulb failing during the hour is:
1 - (probability of both functioning) = 1 - (3/50) = 47/50

Therefore, the probability that the flashlight will perform reliably for one hour is:
1 - (probability of failure) = 1 - (47/50) = 3/50 = 0.8736

Thus, option (C) is correct.

The Readylite Company Produces a Flashlight Which Is Perfectly Reliable