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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 hearts, your friend will pay you $600 Otherwise, you have to pay your friend $36. What is the expected value of your bet? Round your answer to two decimal places. Losses must be expressed as negative values.

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 stand class=

Respuesta :

Answer:

$1.41

Explanation:

• In a standard deck, there are a total of 52 cards; and

,

• The number of Hearts = 13

First, we find the probability of drawing two hearts without replacement.

[tex]\begin{gathered} P(1st\text{ Heart)=}\frac{13}{52} \\ P(2nd\text{ Heart)=}\frac{12}{51} \\ P(\text{two hearts)}=\frac{13}{52}\times\frac{12}{51}=\frac{1}{17} \end{gathered}[/tex]

Next, find the probability of not drawing two hearts.

[tex]P(\text{not drawing two hearts)}=1-\frac{1}{17}=\frac{16}{17}[/tex]

So, we have that:

• You gain $600 with a probability of 1/17.

,

• You lose $36 with a probability of 16/17.

The expected value of your bet therefore is:

[tex]\begin{gathered} (600\times\frac{1}{17})+(-36\times\frac{16}{17}) \\ =\$1.41 \end{gathered}[/tex]

The expected value is $1.41.

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