1.Three students volunteer for a taste test comparing Coke and Pepsi.Each student tastes samples in two identical-looking cups and decides which beverage he or she prefers.

Assume that the students make selections independently of one another.Suppose the probability of picking Pepsi is 3/5 and the probability of picking Coke is 2/5 for all three students.The tasters are referred to as first, second and third.One possible outcome of the experiment is that the first and second students pick Pepsi and the third student picks Coke.The probability of this occurring is 3/5 x 3/5 x 2/5.

Let the random variable x equal the number of Pepsi selections for any given outcome of the experiment.

• Construct a tree diagram and sample space for the outcomes of the experiment.

(HINT:There should be a total of 8 outcomes.)

• Define the probability distribution with X=number of Pepsi selections of an outcome.
• Calculate the mean (expected value) and standard deviation of the distribution.
• Interpret the meaning of the mean and standard deviation.

2.

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.