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