Question

At a gas station where people can pay in cash or by credit card, 20% of people pay by credit card and 80% of people pay cash. A gallon of gas costs $4.00 if paid by card and $3.50 if paid by cash. What is the expected revenue for a gallon of gas sold at this station?

Answer 1

Answer: The expected revenue for a gallon of gas sold at this station is $3.60.

Explanation:

Since we have given that

Percentage of people who pays by credit card = 20%
`=x_1`= 0.2

Percentage of people who pays by cash =
`x_2=` 80% = 0.8

Cost of a gallon of gas paid by card
`=p(x_1)` = $4.00

Cost of a gallon of gas paid by cash =
`p(x_2)=`$ 3.50

So, Expected revenue for a gallon of gas sold at this station is given by

`E(x)=\sum xp(x)`

so, it becomes,

`E(x)=0.2* 4+0.8* 3.5\\\\E(x)=0.8+2.8\\\\E(x)=\$3.60`

Hence, the expected revenue for a gallon of gas sold at this station is $3.60.

Answer 2

A gallon of gas costs:
- $4.00 if paid by card,
- $3.50 if paid by cash.
0.2 * 4.00 + 0.8 * 3.50 = 0.8 + 2.8 = $3.60
Answer:
The expected revenue for a gallon of gas is $3.60.