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

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.

Answer 2

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

Step-by-step 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,

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

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