Statistics:Probability?

Suppose you want to play a carnival game that costs 4 dollars each time you play. If you win, you get $100. The probability of winning is 3/100. What is the expected value of the amount the carnival stands to gain?1. 1.202. 1.103. 1.4. 1.305. 1.506. None of the above. PLEASE SHOW EVERY STEP

For every 100 plays the carny takes in 400 and gives out 300.400 - 300 = 100 (per 100 plays)Therefore, the carny makes 100 for every 100 plays...so the carny makes 1 for every play.

Its (.97 x 4) - (100 x .03)Thats the probability of the event times its effect and then added and subtracted accordingly.3.88 - 3.88 is how I calculate it.Edit: People above me. Every hundred plays they pull in 388 dollars. That is for dollars 97 times. They pay out 100 dollars three times. Please explain how thats not the case. Im very curious.

Mr. Lawrence, you are taking in on the fact that when the customer wins the prize, they still have to pay $4 to win.

The formula to use is "Expected return to player" which is E(x) = x.p(x) where x is the return to player if they winand p(x) is the probability of winning.So here,x = $100 (return to player for winning)p(x) = 3/100 (probability of winning)Therefore expected return to player isE(x) = x.p(x) = $100 x 3/100 = $300/100 = $3Cost: $4Expected return to player is $3. Therefore Loss (to player) is Cost minus Expected return= $4 - $3 = $1