You are playing the new Lemon Game at Vegas. There are 3 windows in the slot machine. Window 1 displays only one of two choices: lemon or strawberry. Window 2 can display three choices: lemon, strawberry, or blueberry. Window 3 can display three choices: lemon, papaya, or cherry. Windows spin randomly and independent from each other. To win $1 you must have one lemon showing. To win $2, you must have two lemons, and to win the $5 jackpot, you must have all windows showing lemons. Using a tree diagram, determine the sample space. Determine the probability distribution. Let the random variable X represent the number of lemons displayed during one spin. Calculate the mean and standard deviation of the distribution. In four sentences or less, would you want to play this game if it cost $.50 per spin? Justify your answer using the expected value approach.
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.
You are playing the new Lemon Game at Vegas. There are 3 windows in the slot machine. Window 1 displays only one of two choices: lemon or strawberry. Window 2 can display three choices: lemon, strawberry, or blueberry. Window 3 can display three choices: lemon, papaya, or cherry. Windows spin randomly and independent from each other. To win $1 you must have one lemon showing. To win $2, you must have two lemons, and to win the $5 jackpot, you must have all windows showing lemons.
Using a tree diagram, determine the
Determine the probability distribution. Let the random variable X represent the number of lemons displayed during one spin.
Calculate the mean and standard deviation of the distribution.
In four sentences or less, would you want to play this game if it cost $.50 per spin? Justify your answer using the
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