risk

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

(.269)*(.64)*(.461)*(.86)*(.55)*(.921)=. 0346=3.46%

b. Consider only the games in February. What is the probability that penn loses ONLY ONE of the February games? Be sure to show your work. (Hint: they could lose against Villanova AND win the others OR they could lose against Houston AND win the others...)

P (Villanova win)=73.1%*64%*46.1%*86%=18.55%

P (Houston win)=26.9%*36%*46.1%*86%=3.84%

P (Tulsa win)=26.9%*64%*53.9%*86%=7.98%

P (UCF win)=26.9%*64%*46.1%*14%=1.11%

P (Temple loses only 1 game Feb)= 18.55%+3.84%+7.98%+1.11%=31.48%

3. Refer to Topic 4 article “How Long a Shot Is Powerball”. 
In Figure 1, the probabilities for each combination of White Balls and Powerball are listed. Is the probability for each result (each White Balls/Powerball combination) an a priori probability or a statistical probability? Justify your answer.

The probability for each result is a statistical probability, because it looked at past date and estimate to come up with the mutuality table.

4. On Thursday, Amazon-Fresh is going to deliver a box of groceries to Restaurant A [Delivery A]. According to their contract, the promised time for delivery is 5:00AM. If the delivery arrives late, Amazon-Fresh will pay $15 penalty to Restaurant A. Based on past experience with the delivery, Amazon-Fresh estimates that this delivery has a 10% of chance of arriving late. 
Derive the probability distribution for total dollar losses. Note that is total dollar losses, not number of losses. Make sure that you label your table correctly. [2 points]

5. On Friday, Amazon-Fresh is going to deliver another box of groceries to Restaurant B [Delivery B]. According to their contract, the promised time for delivery is 6:00AM. If the delivery arrives late, Amazon-Fresh will pay $20 penalty to Restaurant B. Based on past experience with the delivery, Amazon estimates that this delivery has a 20% of chance of arriving late.

a. What are the possible outcomes for Amazon’s total dollar amount of losses for delivery 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.

For $0 loss to occur = P (A and B both arrive in time)

For $15 loss to occur = P (A does not arrive in time and B does)

For $20 loss to occur = P (A arrives in time and B does not)

For $35 loss to occur = P (A and B both did not arrive in time)

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

For $0 loss to occur = P (A and B both arrive in time)

P (A arrives in time)*P (B arrives in time)

(90%)*(80%)=72%

For $15 loss to occur = P (A does not arrive in time and B does)

P (A does not arrive in time)*P (B arrives in time)

(10%)*(80%)=8%

For $20 loss to occur = P (A arrives in time and B does not)

P (A arrives in time)*P (B does not arrive in time)

(90%)*(20%)=18%

For $35 loss to occur = P (A and B both did not arrive in time)

P (A does not arrive in time)*P (B does not arrive in time)

(10%)*(20%)=2%

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