In the casino card game blackjack the dealer gets two cards

In the casino card game blackjack the dealer gets two cards, one of which you can see and one that is upside down. Each player also gets two cards. When the dealer\'s visible card is an ace, she offers you to take out \"insurance\": you can bet $1 that the invisible card is a face card or a 10. If it is, you get $2, otherwise you lose your $1. What is the expected value of the bet (a) if we assume the dealer\'s other card was chosen from a second deck of 52? (b) if we know that both of the dealer\'s cards and our own 6 and 8 came from the same deck of 52 cards.

Solution

a)

Probability of winning the bet (K,Q,J,10) = 16 / 52 = 0.3

Probability of loosing the bet = 1-0.3 = 0.7

b)

Probability of winning the bet (K,Q,J,10) = 16/49 = 0.326

Probability of loosing the bet = 1-0.326 = 0.674