Let 13 cards be taken, at random and without replacement, from an ordinarydeck of playing cards. If X is the number of spades in these 13 cards, find the pmf ofX. If, in addition, Y is the number of hearts in these 13 cards, find the probabilityP(X = 2, Y = 5). What is the joint pmf of X and Y ?
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.
Let 13 cards be taken, at random and without replacement, from an ordinary
deck of playing cards. If X is the number of spades in these 13 cards, find the pmf of
X. If, in addition, Y is the number of hearts in these 13 cards, find the probability
P(X = 2, Y = 5). What is the joint pmf of X and Y ?
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