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Probability: Fair Coin, Danville Population

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1. A fair coin is tossed 4 times. What is the probability that heads show up an even number of times (i.e., never, or twice, or all 4 times).

2. The population of Danville is 20,000. Can it be said with certainty that there must be two or more people in Danville with exactly the same three initials?

3. What is the total possible number of deals in a bridge game? A deal is a distribution of 52 cards to four players, each receiving 13 cards.

4. A group of six men and 12 women are partitioned into six committees of three people each. What is the probability that each committee contains a male member?

5. In a five-card poker game, a straight is five cards in a sequence, but not all of the same suit. A straight flush is five cards in a sequence, all of the same suit. Find the probabilities of obtaining a straight hand or a straight flush.

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