Question

You randomly shuffle a 52-card deck of cards. We will consider what happens as we draw 3 cards from the deck to form a sequence of cards (for a - c) or a set of cards (d).

Answer each of the following questions, showing all relevant calculations. You should analyze these using tree diagrams, but no need to show the diagrams in your answer.

(a) Suppose you draw three cards from the deck with replacement; what is the probability that the first card is red, the second is a spade, and the third is a facecard (Jack, Queen, or King)? [Hint: these are ordered!]

(b) Suppose you draw three cards from the deck with replacement; what is the probability that the first and third cards have the same color, but the second is a different color?

(c) Repeat (b), but without replacement (cards are not put back). [Hint: a tree diagram might be useful.]

Answer 1

(a) Suppose you draw three cards from the deck with replacement; what is the probability that the first card is red, the second is a spade, and the third is a facecard (Jack, Queen, or King)?

There are 26 red cards, 13 spade cards, and 12 face cards in a standard deck of 52 cards.

(b) Suppose you draw three cards from the deck with replacement; what is the probability that the first and third cards have the same color, but the second is a different color?

There are 26 red cards and 26 black cards.

(c) Repeat (b), but without replacement (cards are not put back).