Chapter 13, Problem 24SGR

To determine

If two dice are rolled then find the probability that the sum of the numbers is 7 or 11.

Answer to Problem 24SGR

The probability of getting the sum 11 or sum 11 is $\frac{2}{9}$ .

Explanation of Solution

Given information: It is given that two dice are rolled simultaneously.

Calculation: When two dice are rolled simultaneously then the ordered pair for sum 7 and sum 11 is written as $\left(1,6\right),\left(2,5\right),\left(3,4\right),\left(4,3\right),\left(5,2\right),\left(6,1\right)$ and $\left(5,6\right),\left(6,5\right)$ respectively. Also the sample space will be 36 or (6²) when two dice are rolled simultaneously.

  $\begin{array}{c}P\left(7or11\right)=P\left(7\right)+P\left(11\right)\\ =\frac{6}{36}+\frac{2}{36}\\ =\frac{2}{9}\end{array}$

Hence the probability of getting the sum 11 or sum 11 is $\frac{2}{9}$ .