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 spades, your friend will pay you $39. Otherwise, you have to pay your friend $5.Step 1 of 2 :What is the expected value of your bet? Round your answer to two decimal places. Losses must be expressed as negative values.

Answer 1

Answer:

The expected value is $-2.41.

Step-by-step explanation:

Consider the provided information.

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

The probability that both cards are spade is

$\frac{13}{52} \times \frac{12}{51}=0.25 \times 0.235 = 0.0588$

If both cards are spades, your friend will pay you $39. Therefore,

$0.0588(39)=2.2932$

The probability that both cards are not spade is:

$1-0.0588=0.9412$

If both cards are not spades then you have to pay your friend $5. Therefore,

$0.9412(-5)=-4.706$

Here, negative sign represents the losses.

The expected value of your bet is:

2.2932-4.706 = -2.4128

Hence, the expected value is $-2.41.