Chapter 11.3, Problem 7A

Solution

To plot: The cumulative probabilities plot for a given range of sum on two fair dice when rolled.

The cumulative probabilities plot for the given range of sum on two fair dice when rolled are shown below

  

Given:

The cumulative probabilities for the given range of the sum of two fair dice when rolled are shown below

Sum	2 to 4	2 to 6	2 to 8	2 to 10	2 to 12
Cumulative Probability	$\frac{6}{36}$	$\frac{15}{36}$	$\frac{26}{36}$	$\frac{33}{36}$	$\frac{36}{36}$

Plot:

The cumulative probabilities are written in decimal form as shown below (rounded to two decimal places)

Sum	2 to 4	2 to 6	2 to 8	2 to 10	2 to 12
Cumulative Probability	$\frac{6}{36}=0.17$	$\frac{15}{36}=0.42$	$\frac{26}{36}=0.72$	$\frac{33}{36}=0.92$	$\frac{36}{36}=1$

The probability for sum 2 is $=\frac{1}{36}=0.03$

The upper boundary of the sum range are written on x axis and the probabilities are on y-axis and get the following data. Marking the points (Sum, probability) the graph is shown below.

Sum	2	4	6	8	10	12
Probability	0.03	0.17	0.42	0.72	0.92	1