Suppose that you and a friend are playing cards and you decide to make a friendly wager. The bet is that you will draw two cards without replacement from a standard deck. If both cards are spades, your friend will pay you $225. Otherwise, you have to pay your friend $12. Step 2 of 2 : If this same bet is made 738 times, how much would you expect to win or lose? Round your answer to two decimal places. Losses must be expressed as negative values.

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pedrocarratore pedrocarratore · Answer 1 · 2020-06-25T03:30:28+02:00

Answer:

Win $1,423.59

Step-by-step explanation:

There are 52 cards in a deck, 13 of which are spades.

The probability if drawing two consecutive spades without replacement is:

[tex]P(W) = \frac{13}{52}*\frac{12}{51}\\ P(W) = \frac{3}{51}[/tex]

Therefore, there is a 3 in 51 chance of you winning $225 and a 48 in 51 chance of you losing $12.

The expected value for 738 games is:

[tex]E= 738(\frac{3}{51}*225-\frac{48}{51}*12)\\ E=\$1,423.59[/tex]

You are expected to win $1,423.59.