Question

A homeowner finds that there is a 0.15 probability that a flashlight does not work when turned on. If she has three flashlights, find the probability that at least one of them works when there is a power failure. Find the probability that the second flashlight works given that the first flashlight works.

Answer 1

Answer:0.9966

Explanation:

Given

Probability that flash light does not work is
`P_o=0.15`

If owner has 3 three flashlights then

Probability that atleast one of them works
`=1-P(\text{none of them works})`

Probability that flashlight will work
`=1-P_o=1-0.15`

`=0.85`

Required Probability
`=1-0.15* 0.15* 0.15`

`=1-0.003375`

`=0.9966`

Now, Probability that second works given that first works is given by

`P=P(\text{First works})* P(\text{Second works})`

`P=0.85* 0.85`

`P=0.7225`