Suppose that a player draws a card at random from a pack of

Suppose that a player draws a card at random from a pack of cards, and wins $15 if an ace, king, queen, or jack is obtained, and otherwise wins the face value of the card in dollars. What is the expected amount won by the player? Would you pay $9 to play this game?

Solution

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 = $115 (return to player for winning)
p(x) = 3/15 (probability of winning)

Therefore expected return to player is
E(x) = x.p(x)
= $15 x 3/15
= $45/15
= $3

Cost: $9

Expected return to player is $3.
Therefore Loss (to player) is Cost minus Expected return
= $9 - $4 = $5
.
Would you pay $9 to play this game?.

no