1. A game at thefair involves a wheel with seven sectors. Two of the sectors are pink, two of the sectors are orange, two of the sectors are yellow, and one sector is green. Landing on the green sector will give 3 points, landing on the yellow sector will give 1 point; landing on an orange sector will give 0 points, and landing on a pink sector will give -1 point. Let x = the points you have after one spin a. Construct a probability distribution b. If you take one spin, what is your expected value? c. What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values.
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.
1. A game at thefair involves a wheel with seven sectors. Two of the sectors are pink, two of the sectors are orange, two of the sectors are yellow, and one sector is green.
Landing on the green sector will give 3 points, landing on the yellow sector will give 1 point; landing on an orange sector will give 0 points, and landing on a pink sector will give -1 point.
Let x = the points you have after one spin
a. Construct a
b. If you take one spin, what is your expected value?
c. What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using
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