At the beginning of this chapter on page 184 we discussed Te

At the beginning of this chapter on page 184, we discussed Texas hold’em and described the basic rules of the game. Here we examine some of the simplest probabilities asso- ciated with the game. Recall that, to begin, each player is dealt 2 cards face down, called “hole cards,” from an ordinary deck of 52 playing cards, as pictured in Fig. 5.3 on page 193. The best possible starting hand is two aces, referred to as “pocket aces.”

a. The probability that you are dealt pocket aces is 1/221, or 0.00452 to three significant digits. Optional: Verify that probability by applying techniques found in Sec- tion P.5 of Module P (Further Topics in Probability)on the WeissStats CD.

b. Using the result from part (a), obtain the probability that you are dealt “pocket kings.”

c. Using the result from part (a) and your analysis in part (b), find the probability that you are dealt a “pocket pair,” that is, two cards of the same denomination.

Probability for Equally Likely Outcomes (f/N Rule Suppose an experiment has N possible outcomes, all equally likely.An event that can occur in f ways has probability f/N of occurring: that can occur in f ways has probabilily f/N of occurring Number of ways event can occur Probability of an event Total number of possible outcomes

Solution