Two pair or three of a kind? When drawing five cardsrandomly from a deck, which is more likely, two pairsor three of a kind? A pair is exactly two of the samedenomination. Three of a kind is exactly 3 of the samedenomination. (Don’t count three 8’s as a pair—that’s3 of a kind. And don’t count 4 of the same kind as twopair—that’s 4 of a kind, a very special hand.) How couldyou simulate 5-card hands? Be careful; once you’vepicked the 8 of spades, you can’t get it again in thathand.a) Describe how you will simulate a component.b) Describe how you will simulate a trial.c) Describe the response variable.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Two pair or three of a kind? 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.
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