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

1. 20/35(30)=17.142

2. 5/35(60)=17.142

3. 10/35(60)=17.142

Answer 2

Answer: A = 24 , B = 12.85, C = 8.57

Explanation:

Since we have given that

Number of coupons for 1 month = 20

Number of coupons extended for 1.5 months = 10

Number of coupons extended for 2 months = 5

Total number of coupons is given by

`20+10+5=35`

1 month = 30 days

So, Expected value of extended membership = A+B+C

Here, A is given by

`(20)/(35)* 30\\\\=24`

B is given by

`(10)/(35)* 1.5* 30\\\\=12.85`

C is given by

`(5)/(35)* 2* 30\\\\=8.571`

So, The expected value of extended membership is given by

`A+B+C=24+12.85+8.57=45.42`

Hence, A = 24 , B = 12.85, C = 8.57