If the attrition rate of the customer is 5% every year, what is the probability the customer will not be there in year 3?

Question

I want to find out what is the error in my logic: P(employee not being there in year 3) = P (employee dropping out in year 2 or dropping out in year 3) . Note she cannot drop out in year 1 as per the question assumption

=> P(dropping out in year 2) + P(dropping out in year 3) - P(dropping out in year 2 and dropping out in year 3)

P(dropping out in year 2): .05 P(dropping out in year 3): .05 P(dropping out in year 2 and dropping out in year 3): 0

Based on this, the answer should be 10%, but the correct answer is 9.75%. What did I do wrong?

Answer 1

The mistake you are making is in computing the probability that that the employee drops out in the third year. In order to drop out in the third year, the employee must not have dropped out in the second year, so that the probability of dropping out in the third year is not $.05$ but $$.95\cdot.05 = .0475$$