1. The Pennstate men’s basketball team is playing UCF on Sunday February 25, 2018. Suppose that Temple has a 36.5% chance of winning the game. College basketball games cannot end in a tie.

a. What is the random variable associated with this game? [1 point]

b. What is the mutually exclusive event in this case? [1 point]

c. Construct a well-labeled probability distribution table based on the outcomes of this game. [2 points]

2. Temple will play Date GAME Win Probability1 February 25 UCF 36.5% February 28 UConn 32.0% March 4 Tulsa 25.0%

a. What is the probability that Temple wins ALL remaining games in the regular season (all the ones listed in the above table)? [2 points]

b. Consider ALL games listed. What is the probability that Temple loses ONLY ONE of the remaining games? Be sure to show your work. (Hint: they could lose against UCF AND win the others OR they could lose against UConn AND win the others…) [4 points]

3. On Thursday, ABC Grocery is expecting to receive one package [Package A] containing $350 worth of food. Based on his past experience with the delivery service, the manager estimates that this package has a chance of 30% being lost in shipment. On Friday, ABC Grocery expects another package [Package B] to be delivered. Package B contains $500 worth of food. This package has a 15% chance of being lost in shipment.

a. What are the possible outcomes for ABC Grocery’s total dollar amount of losses for package A and B? For each dollar amount of loss, describe under what circumstances it would occur. In other words, what has to happen in order for each dollar amount of losses to occur? Please note that this asks about total dollar amount of losses, not number of losses. [4 points]

b. For each of the possible outcomes you identify in part [a], derive the probability of the outcome occurring. [2 points]

c. Construct [in table form] the probability distribution for total dollar amount of losses for package A and B. [2 points]

d. Calculate the expected value of total dollar amount of losses. What are the units of measurement? [2 points]

e. The manager has calculated the variance for the total dollar amount of losses to be 57600. Since you want to be sure you are using correct numbers in your evaluation, prove that the manager calculated the correct variance for total dollar amount of losses. Show all work! What are the units of measurement? [4 points]