Question

Using the previous tutorial, address the following: Imagine an experiment where three dice are tossed and the numbers 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=8?

a. Probability is approximately 5%
b. Probability is approximately 10%
c. Probability is approximately 20%
d. Probability is approximately 25%
17. What is the (approximate) probability that Die1+Die2+Die3<7?

a. Probability is approximately 5%
b. Probability is approximately 10%
c. Probability is approximately 15%
d. Probability is approximately 20%
18. What is the (approximate) probability that Max(Die1,Die2,Die3)=5? Careful: Use “Max( ) function in Excel.

a. Probability is approximately 5%
b. Probability is approximately 15%
c. Probability is approximately 25%
d. Probability is approximately 45%

Answer 1

Computation in Excel:

• First draw random sample using command : "=RANDBETWEEN(1,6)"
• Output will be a single number randomly selected between 1 to 6.
• Extend (by dragging) to 1000 rows and three columns denoting three die's outcome.
• Once obtained fix the numbers by simply copy+paste into another sheet and "Keep values only"

This image gives the probabilities:

From above image, we get answers as:

16. What is the (approximate) probability that Die1+Die2+Die3=8?
b. Probability is approximately 10%

17. What is the (approximate) probability that Die1+Die2+Die3<7?
b. Probability is approximately 10%

18. What is the (approximate) probability that Max(Die1,Die2,Die3)=5?
c. Probability is approximately 25%

For Histogram:

Edit the X-axis

Once editing of X-axis is done, appropriate changes like deleting the gridlines, making gap between bars as zero can be done by Right click on chart area and bars respectively.

Finally the histogram is obtained.

Table required for histogram

Lower   Upper   Frequency
0   3   0
3   4   5
4   5   14
5   6   36
6   7   38
7   8   71
8   9   106
9   10   120
10   11   122
11   12   125
12   13   116
13   14   85
14   15   54
15   16   56
16   17   32
17   18   13
18   19   7
19   20   0

Histogram is as follows: