Problem 1 Suppose you have a bag filled with 60 marbles of the same size. 14 of the marbles are catseyes, 8 are alleys, 10 are tri-lites, 12 are aggies, and 16 are clearies. Suppose you draw two marbles from the bag in quick succession, noting the marble type for each draw. Consider the following events: Y1 = {"1st marble is a clearie"} • X1 = {*1t marble is not a clearie"} Y2 = {"2nd marble is a clearie"} • X2 = {"2nd marble is not a clearie"} Do the following: a) Find P(Y2|Y+), P(X2\X1), P(Y2|X1), and P(X2|Y1) b) Find P(Y1), P(X1), P(Y2), and P(X2) c) Find P(Y|Y2), P(X1|X2), P(X;|Y2), and P(Y1|X2)
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.
Parts a , b & c
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