Question

Merry and bright? A string of Christmas lights contains 20 lights. The

lights are wired in series so that if any light fails, the whole string will go dark. Each light has probability 0.98 of working for a 3-year period. The lights fail independently of each other. Find the probability that the string of lights will remain bright for 3 years.

Short answer

The required probability is$0.6676$

Step-by-step solution

Given information

Given that,

Probability of success $\left(p\right)=0.98$

The failure of light is unrelated to the failure of other lights.

Calculation

The probability that the string of lights will remain lit for three years is calculated as follows:

$P(Lightswillbebrightfor20years)={(0.98)}^{20}=0.6676$

Therefore, the required probability is$0.6676$