Question

1. (25 total points) Probability and card games; Recall that an ordinary decdk of playing cards has 52 cards of which 13 cards are from each of the four suits hearts, diamonds, spades, and clubs. Each suit contains the cards 2 to 10, ace, jack, queen, and king. (a) (10 points) Three cards are randomly selected, without replacement, from an or- dinary deck of 52 playing cards. Compute the conditional probability that the first card selected is a spade, given that the second and third cards are spades. (Note that order matters in this problem.) (b) (15 points) A Yarborough hand in bridge is one in which no card is higher than a nine (no aces, tens, jacks, queens, nor kings). Lord Yarborough, for whom this hand was named, bet 1000 to 1 against any given hand being so bad. Given you are dealt 13 cards from an ordinary deck of 52 playing cards, what is the probability of you getting a Yarborough hand? Are the odds (1000 to 1) provided by Lord Yarborough fair to you, why or why not?

Answer 1

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