Chapter 12.7, Problem 7PPS

To determine

To Find :The probability of rolling a 7 with 2 six-sided dice 2 out of 10 times.

Answer to Problem 7PPS

The required probability is 0.75.

Explanation of Solution

Given information:

Two dice are rolled.

Following is the sample space when we roll two dice,

  $S=\left\{\begin{array}{l}\left(1,1\right),\left(1,2\right),\left(1,3\right),\left(1,4\right),\left(1,5\right),\left(1,6\right),\hfill \\ \left(2,1\right),\left(2,2\right),\left(2,3\right),\left(2,4\right),\left(2,5\right),\left(2,6\right),\hfill \\ \left(3,1\right),\left(3,2\right),\left(3,3\right),\left(3,4\right),\left(3,5\right),\left(3,6\right),\hfill \\ \left(4,1\right),\left(4,2\right),\left(4,3\right),\left(4,4\right),\left(4,5\right),\left(4,6\right),\hfill \\ \left(5,1\right),\left(5,2\right),\left(5,3\right),\left(5,4\right),\left(5,5\right),\left(5,6\right),\hfill \\ \left(6,1\right),\left(6,2\right),\left(6,3\right),\left(6,4\right),\left(6,5\right),\left(6,6\right)\hfill \end{array}\right\}$

Each trial is a roll of two dice. The number of trials is 10.

The success is sum 7 of two dice. Out of 36 outcomes, 6 outcomes have sum 7.So the probability of success is

  $\begin{array}{l}s=\frac{6}{36}\\ =\frac{1}{6}\end{array}$

Following table shows the result of 4 simulations (each simulation result 10 trials),

Roll	1	2	3	4	5	6	7	8	9	10	Totalsuccess
Simulation1	f	f	f	f	f	f	f	s	f	f	2
Simulation2	f	s	f	f	f	f	f	s	f	f	2
Simulation3	f	f	s	f	f	f	f	f	s	f	2
Simulation4	f	f	f	f	f	f	f	f	f	f	0

Outof4simulation, 3 simulations shows 2 success (2 7's)out 10sotheexperimentalprobabilityis

  $\begin{array}{l}p=\frac{3}{4}\hfill \\ =0.75\hfill \end{array}$

Hence, the required probability is 0.75.