Q1. Blackjack Table
A standard deck of playing cards contains 52 cards divided equally into four suits: Spades, Hearts, Diamonds, and Clubs. Each suit contains thirteen cards: 2, 3, 4, 5, 6, 7, 8, 9, 10, J(ack), Q(ueen), K(ing), A(ce).
You walk up to the blackjack table at your local casino and ask to be dealt in. You are dealt two cards, the 5 of hearts and the 7 of spades. You see that the dealer also has two cards. One is face down, and the other is the 6 of clubs. You decide to let it ride and hope the dealer busts. The dealer's hidden card is revealed to be the 8 of clubs, making the dealer's hand worth 14 points.
What is the probability that the dealer busts? You may assume that the dealer is usign only 1 deck, and that you have not observed the values of any other cards.
Q2. Sadistic Tendencies
You are captured by a Russian spy and tortured for information. Every time you fail to answer his question adequately, he plays the following game: First, he draws a number randomly between 1 and 4. This becomes the comparison value.
He then draws a number from between 0 and 4. If it is greater than or equal to the comparison value, you get a lash with a wet noodle, and he draws again. He continues this until he draws a number that is less than the comparison value, at which point he continues his interrogation. If he draws a 3 as the comparison value, what is the expected number of lashes you will receive for that question? What is the expected number of lashes you will receive per question?