Chapter 6, Problem 1SR

The possible outcomes of an experiment involving the roll of a six-sided die are a one-spot, a two-spot, a three-spot, a four-spot, a five-spot, and a six-spot

1. (a) Develop a probability distribution for the number of possible spots.
2. (b) Portray the probability distribution graphically.
3. (c) What is the sum of the probabilities?

To determine

Give a probability distribution for the number of possible spots.

Answer to Problem 1SR

The probability distribution for the number of possible spots is as follows:

Number of spots	Probability
1	0.16667
2	0.16667
3	0.16667
4	0.16667
5	0.16667
6	0.16667
Total	1

Explanation of Solution

The outcomes of the experiment are one-spot, two-spot, three-spot, four-spot, five-spot, and six-pot. Thus, there are 6 possible outcomes. The experiment involves the roll of six-sided die. Hence, each outcome has probability of one-sixth.

The probability distribution for the number of possible spots is as follows:

Number of spots	Probability
1	$\frac{1}{6}=0.16667$
2	$\frac{1}{6}=0.16667$
3	$\frac{1}{6}=0.16667$
4	$\frac{1}{6}=0.16667$
5	$\frac{1}{6}=0.16667$
6	$\frac{1}{6}=0.16667$
Total	1

Thus, the probability distribution for the number of possible spots is obtained.

To determine

Show the probability distribution graphically.

Answer to Problem 1SR

The graph of the probability distribution is as follows:

Explanation of Solution

Step-by-step procedure to plot probability distribution graph using EXCEL:

• Enter the probability values in a column.
• Select the data and go to Insert.
• In Charts, select 2-D Column.

Thus, the probability distribution graph is obtained.

To determine

Calculate the sum of the probabilities.

Answer to Problem 1SR

The sum of probabilities is 1.

Explanation of Solution

The sum of probabilities is calculated as follows:

$\begin{array}{c}Sumofprobabilities=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\\ =\frac{6}{6}\\ =1\end{array}$

Therefore, the sum of probabilities is 1.