A standard deck of 52 cards consists of 4 suits with 13 cards each. Two of the suits, clubs and spades, black while the other two suits, hearts and diamonds, are red. Each suit consists of an ace (A), a 2, 3, 4, 5, 6, 7, 8, 9, 10, jack (J), a queen (Q), and a king (K). Thus, there are 4 of each type of card (i.e. a 3 or Q), one of each suit, in the deck. An experiment consists of drawing two cards with replacement (i.e. the person puts the card back and shuffles sufficiently). Answer the following questions: (a) Suppose after drawing each card the experimenter writes down the color (red or black) of the card only. Write out the sample space. (Be careful! The order in which they are drawn matters!) (b) Suppose now that the experimenter records the exact card (e.g. 2 of hearts or K of diamonds). How many outcomes are possible?
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.
A standard deck of 52 cards consists of 4 suits with 13 cards each. Two of the suits, clubs and spades,
black while the other two suits, hearts and diamonds, are red. Each suit consists of an ace (A), a 2, 3, 4, 5,
6, 7, 8, 9, 10, jack (J), a queen (Q), and a king (K). Thus, there are 4 of each type of card (i.e. a 3 or Q),
one of each suit, in the deck. An experiment consists of drawing two cards with replacement (i.e. the
person puts the card back and shuffles sufficiently). Answer the following questions:
(a) Suppose after drawing each card the experimenter writes down the color (red or black) of the card
only. Write out the
(b) Suppose now that the experimenter records the exact card (e.g. 2 of hearts or K of diamonds). How
many outcomes are possible?
(c) If the experiment is as described in 5b, write out the following
many outcomes are in this event? (Again, be mindful that order matters!)
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