Question

A fitness center runs a contest for customers who enroll in its annual membership plan. The customers are allowed to draw a coupon from a jar that contains 20 coupons for 1 month of extended membership, 10 coupons for 1.5 months of extended membership, and 5 coupons for 2 months of extended membership. Assuming a month has 30 days, if the expected value of extended membership (in days) on the first draw is given by the expression A + B + C, identify the correct numerical expressions for A, B, and C.

Answer 1

There are 35 coupons in the jar.
The probability to choose coupon for 1 month of extended membership is
`p(A)= (20)/(35) = (4)/(7)`.
The probability to choose coupon for 1.5 months of extended membership is
`p(B)= (10)/(35) = (2)/(7)`.

Answer: With probability
`(4)/(7)` a customer will get 30 days extended membership,
with probability
`(2)/(7)` a customer will get 450 days extended membership,
with probability
`(1)/(7)` a customer will get 60 days extended membership.
The probability to choose coupon for 1 month of extended membership is
`p(C)= (5)/(35) = (1)/(7)`.
Together P(A)+P(B)+p(C)=1.