Question

The probability that a bearing fails during the first month of use is 0.12. what is the probability that it does not fail during the first month?

Answer 1

The probability that a bearing fails during the first month of use is 0.12. what is the probability that it does not fail during the first month?

Answer: We are given that a bearing fails during the first month of use is 0.12.

We are required to find the probability that the bearing does not fail during the first month of use.

The event that a bearing does not fail during the first month is a complement to the event that a bearing fails during the firs month.

Therefore, we have:

$P(does-not-fail)= 1- P(fails)$

                               $=1-0.12$

                               $=0.88$

Therefore, the probability that bearing does not fail during the first month is 0.88

Complement rule of probability:

The complement rule is stated as "the sum of the probability of an event and the probability of its complement is equal to 1," and is expressed mathematically as:

$P(A)+P(A^{c})=1$ $\implies P(A^{c})=1-P(A)$