Chapter 7.3, Problem 7.62E

(a)

To determine

To Calculate: the probability that a player rolls doubles on a turn.

Answer to Problem 7.62E

0.1667

Explanation of Solution

Given:

Two six sided dice

Formula used:

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

Calculation:

Second dice
		1	2	3	4	5	6
First dice	1	D	N	N	N	N	N
	2	N	D	N	N	N	N
	3	N	N	D	N	N	N
	4	N	N	N	D	N	N
	5	N	N	N	N	D	N
	6	N	N	N	N	N	D

D = represents doubles and N represents non doubles

  $\begin{array}{c}\text{P}\left(\text{doubles}\right)\text{=}\frac{\text{6}}{\text{36}}\\ \text{=0}\text{.1667}\end{array}$

(b)

To determine

To Calculate: the probability that he has to pay $50 to get out of jail because he doesn’t roll double on three consecutive turn.

Answer to Problem 7.62E

0.5787

Explanation of Solution

Given:

Two six sided dice

Formula used:

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

Calculation:

Second dice
		1	2	3	4	5	6
First dice	1	D	N	N	N	N	N
	2	N	D	N	N	N	N
	3	N	N	D	N	N	N
	4	N	N	N	D	N	N
	5	N	N	N	N	D	N
	6	N	N	N	N	N	D

D = represents doubles and N represents non doubles

  $\begin{array}{c}\text{P}\left(\text{No doubles}\right)=1-\text{P}\left(\text{doubles}\right)\\ =1-\frac{6}{36}\\ =\frac{5}{6}\end{array}$

  $\begin{array}{c}\text{P}\left(\text{No doubles on three consecutive rolls}\right)\\ =\text{P}\left(\text{No doubles}\right)\times \text{P}\left(\text{No doubles}\right)\times \text{P}\left(\text{No doubles}\right)\\ =\frac{5}{6}\times \frac{5}{6}\times \frac{5}{6}\\ =\frac{125}{216}\\ =0.5787\end{array}$