III.9. 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 |
| Probability: | 0.50 | 0.42 |
| Hand: | Two pairs | Better hands |
| Probability: | 0.05 | ? |
(a) What must be the probability of getting a hand better than two pairs? (Hint: See page 429.)
(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 two repetitions. (Hint: See page 472.)