Chapter 2.5, Problem 18PSC

a)

To determine

To calculate: P (Sum is less than ${90}^{\circ }$ )

Answer to Problem 18PSC

  $\frac{2}{9}$

Explanation of Solution

Given Information: Ten angle are given whose measure are as follows :

  $\{{30}^{\circ },{30}^{\circ },{30}^{\circ },{30}^{\circ },{60}^{\circ },{60}^{\circ },{60}^{\circ },{90}^{\circ },{90}^{\circ },{120}^{\circ }\}.$

Formula: probability = Numbers of favorable outcomes / total numbers of outcomes.

Calculation:

Sum is less than ${90}^{\circ }$ if angle are $({30}^{\circ },{30}^{\circ })$ only, Which has 6 possible case

Hence probability = $\frac{6}{45}=\frac{2}{9}$

b)

To determine

To calculate: P (angles are complementary)

Answer to Problem 18PSC

  $\frac{4}{9}$

Explanation of Solution

Given Information: Ten angle are given whose measure are as follows :

  $\{{30}^{\circ },{30}^{\circ },{30}^{\circ },{30}^{\circ },{60}^{\circ },{60}^{\circ },{60}^{\circ },{90}^{\circ },{90}^{\circ },{120}^{\circ }\}.$

Formula: probability = Numbers of favorable outcomes / total numbers of outcomes.

Calculation:

Angles are complementary if one angle is ${30}^{\circ }$ and other is ${60}^{\circ }$ which has possible outcomes

Hence probability = $\frac{12}{45}=\frac{4}{9}$