# Thread: HELP, cant figure it out.

1. ## HELP, cant figure it out.

Once a year employees at a company are given the opportunity to join one of three pension plans, A, B, or C. Once an employee decides to join one of these plans, the employee cannot drop the plan or switch to another plan. Past records indicate that each year 12% of the employees elect to join plan A, 5% elect to join plan B, 4% elect to join plan C, and the remainder to not join any plan. (1) In the long run, what percentage of employees will elect to join plans A, B, and C? (2) On average, how many years will it take an employee to decide to join a plan? (1) % of employees will elect to join plan A. (Type an integer or decimal. Round to the nearest tenth.)

2. ## Re: HELP, cant figure it out.

Plan A:
$$.12\sum_{n=0}^\infty (.79)^n = \dfrac{.12}{.21}$$

Plan B:
$$\dfrac{.5}{.21}$$

Plan C:
$$\dfrac{.4}{.21}$$
(2) expected value of number of years to join a plan
$$.21\sum_{n=1}^\infty n (.79)^{n-1} = \dfrac{.21}{(.21)^2}=\dfrac{1}{.21}$$