Question

Using the previous tutorial, address the following: Imagine an experiment where three dice are tossed and the number on each die is recorded under Die1, Die2, and Die3. Answer the following questions about the sum of the three numbers recorded from: Die1+Die2+Die3. (Discussions allowed)

Hint:

• Simulate this experiment 1000 times. (Use the same procedure as in the above tutorial, but for the Number of Variables, instead of 1 put 3, since we are rolling 3 dice not one).
• Next, create a new column by writing in cell D1 =A1+B1+C1, and scroll down the results by clicking on D1 cell and bottom-right corner. (for more detail see the Book chapter on lecture 26)
• Finally create the histogram based on this new column. Use bins 3,4,5,…,18.

16. What is the (approximate) probability that Die1+Die2+Die3=10?

a. The probability is approximately 5%.

b. The probability is approximately 10%.

c. The probability is approximately 20%.

d. The probability is approximately 25%.

17. What is the (approximate) probability that Die1+Die2+Die3>10?

a. The probability is approximately 25%.

b. The probability is approximately 35%.

c. The probability is approximately 50%.

d. The probability is approximately 75%.

18. What is the (approximate) probability that Die1+Die2>9? Careful: You need to create another column (and histogram) based on the first two dice or to argue directly by listing all possible outcomes!

a. The probability is approximately 5%.

b. The probability is approximately 15%.

c. The probability is approximately 25%.

d. The probability is approximately 35%.

Answer 1

16. when three dice are tossed, Possible outcomes with sum= 10 are (1,3,6) (1,4,5) (1,5,4) (1,6,3) (2,6,2)(2,2,6) (2,3,5) (2,4,4) (2,5,3) (3,5,2) (3,1,6)(3,2,5) (3,3,4) (3,4,3) (3,6,1) (4,1,5) (4,2,4) (4,3,3) (4,4,2)(4,5,1) (5,1,4) (5,2,3) (5,3,2) (5,4,1) (6,1,3) (6,2,2)(6,3,1) So, there are 27 outcomes with sum is Die 1+Die2+Die3=10, P (Die 1+Die2+Die 3=10) = 27/1000 = 0.027 = 2.7% 5% Option: A Probability is approximately 5% 17. When three dice are tossed then there are 108 possible outcomes with sum = Die 1+Die 2+Die>10 P (Die1+Die2+Die3=10) = 135/1000 = 0.135 = 13.5% 25% Option: A Probability is approximately 25% 18. The possible outcome for Die1+Die2>9 are (4,6),(5,5),(5,6),(6,4),(6,5),(6,6) P (Die 1+Die2>9) = 6/1000 = 0.0065 % Option: A Probability is approximately 5%