Question

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 0.02 of failing during 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.

Answer 1

To find the probability that the string of lights will remain bright for 3 years, we can use the concept of complementary probability.

Let's calculate the probability that a single light will remain functional for 3 years. The probability that a single light fails in a 3-year period is 0.02. Therefore, the probability that a single light remains functional is 1 - 0.02 = 0.98.

Since the lights are wired in series, for the entire string of lights to remain bright, each individual light must remain functional. Since the lights fail independently of each other, we can multiply the probabilities of each light remaining functional to find the probability that the whole string of lights will remain bright.

The probability that the string of lights will remain bright for 3 years is given by:

P(string remains bright) = (0.98)^20 ≈ 0.6698

Therefore, the probability that the string of lights will remain bright for 3 years is approximately 0.6698 or 66.98%.