Chapter 7.2, Problem 7.29E

To determine

To Calculate: the probability for the each of the following events for doubles, sum of spots showing on the two dice is 10 or less and red die a higher number of spots showing than green.

Answer to Problem 7.29E

For double (the same number of spots showing on both dice) = 0.17

For sum of the spots showing on the two dice is 10 or less = 0.92

For red dice have a higher number of spots showing than green dice =0.42

Explanation of Solution

Formula used:

  $\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}$

Calculation:

For double (the same number of spots showing on both dice)

Dice 1
		1	2	3	4	5	6
Dice2	1	d
	2		d
	3			d
	4				d
	5					d
	6						d

  $\begin{array}{c}\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}\\ =\frac{6}{36}\\ =0.17\end{array}$

For sum of the spots showing on the two dice is 10 or less

Dice 1
		1	2	3	4	5	6
Dice2	1	m	m	m	m	m	m
	2	m	m	m	m	m	m
	3	m	m	m	m	m	m
	4	m	m	m	m	m	m
	5	m	m	m	m	m
	6	m	m	m	m

  $\begin{array}{c}\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}\\ =\frac{33}{36}\\ =0.92\end{array}$

For red dice have a higher number of spots showing than green dice

Dice 1
		1	2	3	4	5	6
Dice2	1		r	r	r	r	r
	2			r	r	r	r
	3				r	r	r
	4					r	r
	5						r
	6

  $\begin{array}{c}\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}\\ =\frac{15}{36}\\ =0.42\end{array}$