4.54 Texas hold ’em. The game of Texas hold ’em starts with each player receiving two cards. Here is the probability distribution for the number of aces in two-card hands:

Number of aces 0 1 2
Probability 0.8507 0.1448 0.0045

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    (a) Verify that this assignment of probabilities satisfies the requirement that the sum of the probabilities for a discrete distribution must be 1.

  2. (b) Make a probability histogram for this distribution.

  3. (c) What is the probability that a hand contains at least one ace? Show two different ways to calculate this probability.