( 12 points ) A statistical experiment involves flipping a fair coin and rolling a fair, six-sided die.

2. (12 points) A statistical experiment involves flipping a fair coin and rolling a fair, six-sided die. Due to a manufacturing error, two sides of the fair die show 4; it has no 5 on it; other four sides show 1, 2, 3, or 6.

(a) Determine the sample space for the statistical experiment. The sample space is the set of all possible outcomes; for example, 3H, 5T, where the single digit comes from the die and H or T comes from the coin, H standing for Heads and T standing for Tails. The format of your sample space (S) in set notation would look like

S = {1H, 1T, ... }

Hint: You may use a tree diagram or a table to find all possible outcomes in an organized manner to catch all possible outcomes.

(b) If H represents 1 and T represents 2, construct a two-column probability distribution table for the random variable X, representing the total for each possible outcome and its probability (a fraction). For example, for 3H, the value of X would be 3+1 = 4, and for 6T the value of X

would be 6+2 =8.

Hint: Make sure that the probability values (preferably in fractions) in the probability column of your table add up to 1.