Question

A camera's flash mechanism fails on 14% of shots. If 20 shots are taken using the flash, what is the probability that the flash fails exactly twice?

Answer 1

The probability that the flash mechanism fails exactly twice is `C_2^20(.14)^2(1-.14)^18`

Explanation:

Assuming that the flash mechanism failures are independent, this scenario is modeled by the binomial distribution. Since we want to know the probability of the flash failing exactly twice, that probability is `.14^2`. If the flash fails twice, that means the flash works for the other 18 times, giving us the probability of `(1-.14)^18`. Since the flash can fail on any 2 shots out of a total of 20 shots, there are `C_2^20` ways for this to happen. Combining everything, we end up with `C_2^20(.14)^2(1-.14)^18~~0.247`.