Question

# Probabilities with a deck of cards. There are 52 cards in a standard deck of cards....

Probabilities with a deck of cards. There are 52 cards in a standard deck of cards. There are 4 suits (Clubs, Hearts, Diamonds, and Spades) and there are 13 cards in each suit. Clubs/Spades are black, Hearts/Diamonds are red. There are 12 face cards. Face cards are those with a Jack (J), King (K), or Queen (Q) on them. For this question, we will consider the Ace (A) card to be a number card (i.e., number 1). Then for each suit, there are 10 number cards.

(a). What is the probability of drawing a red King, then a black Jack, followed by a red number card without replacement?

(b). In a poker game, a royal flush is a hand consisting of the cards A, K, Q, J, 10 of the same suit. Two players A and B are playing poker with a deck of cards. First, A is dealt a hand (i.e. 5 cards) from the deck without replacement. Then B is dealt a hand (i.e., 5 cards) from the remaining deck without replacement. What is the conditional probability that B also gets a royal flush given that A has a royal flush?

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