Suppose you want to play a carnival game that costs 7 dollars each time you play. if you win, you get $100. the probability of winning is 1⁄50. what is the expected value of the amount that you, the player, stand to gain?

The correct answer would be $5

Explanation:

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 win

and p(x) is the probability of winning.

So here,

x = $100 (return to player for winning)

p(x) = 1/50 (probability of winning)

Therefore expected return to player is

E(x) = x.p(x)

= $100 x 1/50

= $100/50

= $2

Cost: $7

Expected return to player is $2.

Therefore Loss (to player) is Cost minus Expected return

= $7 - $2 = $5 < expected value for the carnival to gain,

The loss to the player is the carnival's gain. It's $5.

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