Question

Fionn observed that 91% of the background checks he processes are for potential employees who have already interviewed. let b be the number of background checks fionn processes to get his first background check for a potential employee who has not yet interviewed for the job. assume that the interview statuses are independent. find the probability that the 8^th background check that fionn processes is the first for which the potential employee has not yet interviewed. you may round your answer to the nearest hundredth. p(b=8)=?

Answer 1

The probability that the 8th background check Fionn processes is the first for which the potential employee has not yet interviewed is approximately 0.4592.

Step-by-step explanation:

To find the probability that the 8th background check Fionn processes is the first for which the potential employee has not yet interviewed, we need to calculate the probability that the first 7 checks are for employees who have already interviewed and the 8th check is for an employee who has not yet interviewed.

Since the interview statuses are independent, the probability that any background check is for an employee who has already interviewed is 91% or 0.91. Therefore, the probability that the 8th background check is for an employee who has not yet interviewed is 1 - 0.91^7 ≈ 0.4592.