Poker. Deal a five-card poker hand from a shuffled deck. The probabilities of several types of hand are approximately as follows:

Hand: Worthless One pair Two pairs Better hands Probability: 0.50 0.42 0.05 ?

(a) What must be the probability of getting a hand better than two pairs? (Hint:

See pages 395–399.)

(b) What is the expected number of hands a player is dealt before the first hand better than one pair appears? Explain how you would use simulation to answer this question, then simulate just 2 repetitions. (Hint: See pages 435–436.)