You have five identical pieces of equipment. There is a 1 in 10 chance that each piece will fail in a year. What is the likelihood that ALL pieces fail in the same year?
To determine the likelihood that all five pieces of equipment will fail in the same year, we need to calculate the probability that each individual piece fails and then multiply those probabilities together.
Since each piece has a 1 in 10 chance of failing in a year, the probability of a single piece not failing in a year is 1 - (1/10) or 9/10. We can use this to calculate the probability that one specific piece fails in a year, which is 1/10 or 1/10.
To determine the probability that all five pieces fail in the same year, we multiply the probabilities together:
(1/10) * (1/10) * (1/10) * (1/10) * (1/10) = 1/10,000
Therefore, the likelihood that all five pieces of equipment will fail in the same year is 1 in 10,000.