Christmas Lights Christmas lights are often designed with

Chapter 5, Problem 16E

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QUESTION:

Problem 16E

Christmas Lights Christmas lights are often designed with a series circuit. This means that when one light burns out the entire string of lights goes black. Suppose that the lights are designed so that the probability a bulb will last 2 years is 0.995. The success or failure of a bulb is independent of the success or failure of other bulbs.

(a) What is the probability that in a string of 100 lights all 100 will last 2 years?

(b) What is the probability that at least one bulb will burn out in 2 years?

Questions & Answers

QUESTION:

Problem 16E

Christmas Lights Christmas lights are often designed with a series circuit. This means that when one light burns out the entire string of lights goes black. Suppose that the lights are designed so that the probability a bulb will last 2 years is 0.995. The success or failure of a bulb is independent of the success or failure of other bulbs.

(a) What is the probability that in a string of 100 lights all 100 will last 2 years?

(b) What is the probability that at least one bulb will burn out in 2 years?

ANSWER:

Solution:

Step 1 of 3:

It is given that bulbs are designed in a series circuit and the failure and success of each bulbs are independent of other bulbs.

Also, it is given that 0.995 is the probability that a bulb will last for 2 years.

Using this we need to find the required values.


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