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 $p(A)= \frac{20}{35} = \frac{4}{7}$.
The probability to choose coupon for 1.5 months of extended membership is $p(B)= \frac{10}{35} = \frac{2}{7}$.

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