There are three generators powering the flood lights on your

There are three generators powering the flood lights on your property, and they all work independently of one another. The generators are old and worn out, and the probability the first one will work through the night is .7, the probability the second one will work through the night is .8, and the probability the third one will work through the night is .65.

a. Find the probability all three generators will work through the night.

b. As long as at least one of the generators is working, the flood lights will remain lit. Unfortunately, this is during the Zombie Apocalypse and you will survive the night if and only if the floodlights remain lit. Find the probability you survive the night.

Solution

a. Find the probability all three generators will work through the night.

Probability will be = 0.7 * 0.8 * 0.65 = 0.364

Find the probability you survive the night.

at least one of the generators is workins is 0.7 + 0.8 + 0.65 - 0.7*0.8 - 0.7*0.65 - 0.65*0.8 +0.7*0.8*0.65 = 0.979