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Problem 16

When drawing five cards randomly from a deck, which is more likely, two pairs or three of a kind? A pair is exactly two of the same denomination. Three of a kind is exactly 3 of the same denomination. (Don’t count three 8’s as a pair—that’s 3 of a kind. And don’t count 4 of the same kind as two pair—that’s 4 of a kind, a very special hand.) How could you simulate 5-card hands? Be careful; once you’ve picked the 8 of spades, you can’t get it again in that hand. a) Describe how you will simulate a component. b) Describe how you will simulate a trial. c) Describe the response variable.

Answer

a)$=\frac{24}{10000}$ b) A trail is 5 card hands. We must examine 10000 two-digit random numbers, and count how many times each outcome appears. Whichever appears the majority of times can be declared as more likely outcome. c) The response variable is whether the outcome of 5 -card hand is $a^{\prime \prime}$ two pairs of a kind" or three of a kind".

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