Question

If the light bulbs in a house fail according to a Poisson law, and over the last 15 weeks there have been 5 failures, find the probability that there will not be more than one failure next week.

Answer 1

Light bulbs in a house fail according to a Poisson law.

Over last 15 weeks the number of failure is 5

So ,the rate of failure is = 5/15 =0.33 per week.

Let, X= number of light bulb failure in a house.

Clearly , X~ Poisson (0.33)

We have to find the probability that,there will not more than 1 failure next week.

That is, P ( X 1) =P ( X=0)+ P ( X =1)

= e​​​​^{​​​​​​-0.33} (0.33)⁰/0! + e ^-0.33(0.33)¹/1

= 0.9561

The required probability is 0.9561​​​​​​^{​​​​​​}