Chapter 11.5, Problem 18PSB

To determine

To Calculate: The probability that both the figures have apothems.

Answer to Problem 18PSB

The probability that both the figures have apothems is $\frac{2}{5}$

Explanation of Solution

Given information: Two figures had been chosen among a scalene triangle, an equilateral triangle, a kite, a square, a regular octagon and a regular hexagon.

Formula used:Here, we are using the formula

Probability = $\frac{Favorableoutcomes}{Totalnumberofoutcomes}$

Calculation: Here, favorable outcomes are $6$ (scalene triangle, an equilateral triangle, a kite, a square, a regular octagon and a regular hexagon)

Here, total number of outcomes are

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

  →Probability = $\frac{Favorableoutcomes}{Totalnumberofoutcomes}$

  → $\frac{6}{15}=\frac{2}{5}$

Conclusion: Hence,the probability that both the figures have apothems is $\frac{2}{5}$