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 diamonds, your friend will pay you $30. Otherwise, you have to pay your friend $4. 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:

Total bet amount= -$2

Explanation:

In a card deck of 52 cards we have 13 diamond cards. Cards are drawn without replacement.

Probability of the first card being diamond = 13/52

Probability of the send card being diamond= 12/51

So the probability for both cards being diamond = (13/52)*(12/51)= 0.0588235

Bet amount for 2 diamonds= probability* amount received

Bet amount for 2 diamonds= 0.0588235* $30= $1.765

Probability of no diamond= 1- 0.0588235

Probability of no diamond= 0.94118

Bet amount for no diamonds= 0.94118* (-$4)

Bet amount for no diamonds= -$3.765

Total bet amount= Bet amount for diamonds + bet amount for no diamonds

Total bet amount= $1.765+ (-$3.765)

Total bet amount= -$2