Question

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 clubs, your friend will pay you $9. Otherwise, you have to pay your friend $3.

What is the expected value of your bet? Round your answer to two decimal places. Losses must be expressed as negative values.

Answer 1

The expected value is $$-2.23$

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

The probability that both cards are spade is

$\frac{13}{52} \times \frac{12}{51} = 0.0588$

If both cards are spades, your friend will pay you $$9$. Therefore, 0$.0588 \times 9 = 0.5292$

Probability that both are not spade $= 1-0.0588 = 0.9412$

If both cards are not spades then you have to pay your friend $$3$. Therefore, $0.9412 \times -3 = -2.8236$

Here, negative sign represents the losses.

The expected value of your bet is: $0.5292-2.8236=-2.2944$

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