Chapter 11, Problem 24STP

To determine

To evaluate: the probability that the results are an even number followed by a number less than 10.

Answer to Problem 24STP

Probability is $\frac{3}{4}$ .

Explanation of Solution

Given:

A fair 12-sided die, labeled from 1 to 12 is twice.

Calculation: -

The number of outcomes that results an even number followed by a number less than 10 are 63.

  $\left[\begin{array}{l}\left(2,1\right),\left(2,2\right)\mathrm{.............}\left(2,9\right)\\ \left(3,1\right),\left(3,2\right)\mathrm{.............}\left(3,9\right)\\ \left(4,1\right),\left(4,2\right)\mathrm{.............}\left(4,9\right)\\ \left(6,1\right),\left(6,2\right)\mathrm{.............}\left(6,9\right)\\ \left(8,1\right),\left(8,2\right)\mathrm{.............}\left(8,9\right)\\ \left(10,1\right),\left(10,2\right)\mathrm{.............}\left(10,9\right)\\ \left(12,1\right),\left(12,2\right)\mathrm{.............}\left(12,9\right)\end{array}\right]$

The total numbers of outcomes are 84.

  $\begin{array}{c}\text{Required probability}=\frac{63}{84}\\ =\frac{21}{28}\\ =\frac{3}{4}\end{array}$

Hence,

Probability is $\frac{3}{4}$ .