Chapter 11.3, Problem 1A

Solution

To calculate: The frequency and probability of getting a sum of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 when two standard dice are rolled.

Sum	Frequency	Probability
2	4	$\frac{3}{100}$
3	6	$\frac{5}{100}$
4	7	$\frac{7}{100}$
5	10	$\frac{10}{100}$
6	11	$\frac{13}{100}$
7	18	$\frac{18}{100}$
8	15	$\frac{15}{100}$
9	12	$\frac{12}{100}$
10	9	$\frac{9}{100}$
11	5	$\frac{5}{100}$
12	3	$\frac{3}{100}$

Given:

The total number of standard dice rolled $=2$ .

The total possibilities of sum of numbers on two dice are $\left\{2,3,4,5,6,7,8,9,10,11,12\right\}$ .

The total number of times two dice are rolled $=100$ .

Concept used:

The theoretical probability is calculated using the formula.

  $\text{Experimental Probability}=\frac{\text{Frequency}}{\text{Total outcomes}}$

Calculation:

The total number of times two dice is 100.

The frequency of each possible sum is noted down and shown below:

Sum	2	3	4	5	6	7	8	9	10	11	12
Frequency	3	5	7	10	13	18	15	12	9	5	3

Thus, with respect to the frequencies, the probabilities of sum when two dice are rolled are shown below:

Sum	Frequency	Probability
2	4	$\frac{3}{100}$
3	6	$\frac{5}{100}$
4	7	$\frac{7}{100}$
5	10	$\frac{10}{100}$
6	11	$\frac{13}{100}$
7	18	$\frac{18}{100}$
8	15	$\frac{15}{100}$
9	12	$\frac{12}{100}$
10	9	$\frac{9}{100}$
11	5	$\frac{5}{100}$
12	3	$\frac{3}{100}$