Chapter 1.9, Problem 1PSA

To determine

To find the probability of the angle to be acute when one of the five angles is selected at random.

Answer to Problem 1PSA

  $TheProbabilityis\frac{3}{5}.$

Explanation of Solution

Given information: The angles can be classified as follows:

  $\begin{array}{l}Acuteangles:40°,50°and60°.\hfill \\ Rightangles:90°.\hfill \\ Obtuseangles:130°. \hfill \end{array}$

Formula used:

Probability means possibility.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Probability of event to happen is

  $P\left(E\right)=Numberoffavourableoutcomes/TotalNumberofoutcomes$

Calculation:

An acute angle is an angle smaller than a right angle. In simple words, acute means small. $Therangeofanacuteangleisbetween0and90degrees.$

  

  

In our example, there are three favorable outcomes, i.e. $40°,50°and60°$

There are five total number of outcomes i.e. $40°,50°,60°,90°and130°.$

Probability that angle is acute will be

  $P\left(Angleisacute\right)=\frac{3}{5}=0.6=60\%.$