Chapter 5.2, Problem 31E

(a)

To determine

To find: the probability model for this possibility process.

Explanation of Solution

Given:

  

There are four-sided die has 4 possible outcomes: 1, 2, 3 and 4, where all 4 outcomes are equally likely to occur

Rolling two fair four-sided dice

Suppose (x, y) show the result of the two dice, where x shows the result of the 1^st die and y show the outcome of the 2^nd die.

First die	Second die
	1	2	3	4
1	(1,1)	(1,2)	(1,3)	(1,4)
2	(2,1)	(2,2)	(2,3)	(2,4)
3	(3,1)	(3,2)	(3,3)	(3,4)
4	(4,1)	(4,2)	(4,3)	(4,4)

(b)

To determine

To Explain: the event A as obtain a sum of 5.

Answer to Problem 31E

  $\frac{1}{4}=0.25=25\%$

Explanation of Solution

Given:

  

Calculation:

There are four-sided die has 4 possible outcomes: 1, 2, 3 and 4, where all 4 outcomes are equally likely to occur

Rolling two fair four-sided dice

Suppose (x, y) show the result of the two dice, where x shows the result of the 1^st die and y show the outcome of the 2^nd die.

First die	Second die
	1	2	3	4
1	(1,1)	(1,2)	(1,3)	(1,4)
2	(2,1)	(2,2)	(2,3)	(2,4)
3	(3,1)	(3,2)	(3,3)	(3,4)
4	(4,1)	(4,2)	(4,3)	(4,4)

The table is having 16 outcomes of which 4 outcomes in a sum of 5, more precisely, these outcomes are (1,4), (2,3),(3,2),(4,1) because 1+4 = 5 and 2+3 = 5.

The probability is

  $\begin{array}{c}P\left(A\right)=\frac{\text{favorable cases}}{\text{total cases}}\\ =\frac{4}{16}\\ =\frac{1}{4}\end{array}$

  $\begin{array}{c}=0.25\\ =25\%\end{array}$