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 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.

Answer 1

$1.41

Step-by-step 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.

`\begin{gathered} P(1st\text{ Heart)=}(13)/(52) \\ P(2nd\text{ Heart)=}(12)/(51) \\ P(\text{two hearts)}=(13)/(52)*(12)/(51)=(1)/(17) \end{gathered}`

Next, find the probability of not drawing two hearts.

`P(\text{not drawing two hearts)}=1-(1)/(17)=(16)/(17)`

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:

`\begin{gathered} (600*(1)/(17))+(-36*(16)/(17)) \\ =\$1.41 \end{gathered}`

The expected value is $1.41.