While playing a board game, Amelia needs to roll a 10-sided die and two 6-sided dice, and calculate their sum. Assume all dice are fair. Let X be the sum of the three dice. Let S1 be the sample space that lists all possible combinations of the 3 dice rolls. Let SX be the sample space of X.

Answer the following questions:

(1):Using the expand.grid() function in R, create the sample space S1. In R, call it S1. Using R code, confirm that S1 has 360 rows.

(2):Calculate the sum of each row of S1. Store all the sums in a variable called X. X should be a vector that contains 360 values, corresponding to the sums of 360 rows in S1. HINT: You might find the function rowSums() helpful.

(3):Last week, we learn about the probability mass function (PMF). The PMF of a discrete random variable X is a list of probabilities for each value of the sample space of X. Using R, find the PMF of X and store it in the variable PMF. You may round the values in the table to 3 decimal places. Include this table in your answer. HINT: See example 2.3.13 from the textbook. 2

(4): Amelia wants the sum of her three rolls to be 20 or higher. Use R to calculate what is P(X 20)? HINT: Use the PMF