Consider the following lottery consisting of similar balls of different color values: Red (R); White (W); Black (B); and Green (G).

The Sample Space for this lottery is the following:

R W W B W G G W B W W G G G R R R B G G

What are the potential outcome values of a selection experiment for this lottery? List them in the following table. Use only as many rows as needed.

Outcome Value

Now, add to this table the number of opportunities for each of the values to be chosen. Remember, "Total" describes all the opportunities to be chosen, which is equal to the size of the Sample Space.

Outcome Value	Opportunity to be chosen
Total

Now, add to this table the relative opportunity for each value to be chosen. That is, the opportunity of that value to be chosen relative to the other values. Express all percentages as decimals (two decimal places).

Outcome Value	Opportunity to be chosen	Relative Opportunity to be Chosen = Opportunity to be Chosen Total
Total

Now, construct the probability distribution table for this random variable. Remember, the probability of each outcome is equal to its relative opportunity to be chosen in this lottery:

Outcome Value	Probability
Total

• (15 points)

Consider the following lottery consisting of similar balls of different dollar values. The Sample Space for this lottery is the following:

6 1 5 1 2 1 3 1 5 6 5 3 4 4 4 3 1 1 3 2 2 1 4 2 2 2 3

What are the potential outcome values of a selection experiment for this lottery? List them in the following table. Use only as many rows as needed.

Outcome Value

Now, add to this table the number of opportunities for each of the values to be chosen. Remember, "Total" describes all the opportunities to be chosen, which is equal to the size of the Sample Space.

Outcome Value	Opportunity to be chosen
Total

Now, add to this table the relative opportunity for each value to be chosen. That is, the opportunity of that value to be chosen relative to the other values. Express all percentages as decimals (two decimal places).

Outcome Value	Opportunity to be chosen	Relative Opportunity to be Chosen = Opportunity to be Chosen Total
Total

Now, construct the probability distribution table for this random variable. Remember, the probability of each outcome is equal to its relative opportunity to be chosen in this lottery:

Outcome Value	Probability
Total

Continuing, find the expected value of the selection experiment. This is calculated as the mean:

Outcome Value	Probability	Contribution to the Mean = Expected Value = Value * Probability
Total

Mean = Expected Value = E(X) = _______________

Finally, find the Expected Variationor Variancefor this selection experiment:

Use the following worktable, and remember that "Diff" = (Outcome Value - E(X)) and "Diff²" = Diff * Diff.

Outcome Value	E(X)	Diff	Diff2	Probability	Contribution = Diff2 * Probability
Total

The Total of the contributions is the Variance = Var (X) = ____________

The Square Root of the Variance is the Standard Deviation = ____________