Question

A person creates a game in which a person pays $5.00 to play. Then, they draw a single card from a standard shuffled deck of cards.

If they draw a face card, they win $10.00 (i.e. they get their $5.00 back and get an extra $5.00).

If they draw an ace, they win $20.00 (i.e. they get their $5.00 back and get an extra $15.00).

With any other draw they lose their money.

What is the expected money value playing this game?


-$5.00

-$1.15

$1.31

$0.38

Answer 1

Explanation:

The expected value is the probability of an event multiplied by the number of times the event happens. And if there is more than 1 event, the expected value is the sum of those.

There are 52 cards in a deck.

There are 12 face cards in a deck. (gain 10)

There are 4 ace in a deck. (gain 20)

Any other card is 36 of them. (lose 5)

The probability of face card is 12/52

The probability of ace is 4/52

The probability of any other card is 36/52

Thus the expected values is:

(12/52)(10) + (4/52)(20) + (36/52)(-5) = $0.38

Answer 2

-$1.15

Explanation:

probability to draw a face card: 12/52

probability to draw an ace: 4/52

probability to lose: (52 - 16)/52 = 36/52

The expected money value is the sum of all possible outcomes, each multiplied by the probability of its occurrence.

$5.00*12/52 + $15.00*4/52 - $5*36/52 = -$1.15