Y Ou are piaying a game involving a fair 6-sided die and a fair coin. First the die is rolled. If the number on the die is evenly divisible by 3 (i.e., either 3 or 6), then the coin is flipped twice, but if the number on the die is not evenly divisible by 3 (i.e., either 1, 2, 4 or 5), then the coin is flipped only once. You win $1 every time head appears on the coin and you win nothing every time a tail appears. On one play of the game, determine the probability that you win some money. Determine the probability that the roll of the die was a 3 or a 6, given that you did win some money.
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.
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