A standard deck of cards is being used to play a game. There are four suits (hearts, diamonds, clubs, and spades), each having 13 faces (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king), making a total of 52 cards. This complete deck is thoroughly mixed, and you will receive the first 2 cards from the deck, without replacement (the first card is not returned to the deck after it is selected).
a. What is the probability that both cards are queens?
b. What is the probability that the first card is a 10 and the second card is a 5 or 6?
c. If you were sampling with replacement (the first card is returned to the deck after it is selected), what would be the answer in (a)?
d. In the game of Blackjack, the face cards (jack, queen, king) count as 10 points, and the ace counts as either 1 or 11 points. All other cards are counted at their face value. Blackjack is achieved if 2 cards total 21 points. What is the probability of getting Blackjack in this problem? Discuss.