Chapter 1.9, Problem 15PSC

a

To determine

The probability that chosen point is in square SQUA.

Answer to Problem 15PSC

The probability that chosen point is in square SQUA is $\frac{1}{5}$

Explanation of Solution

Given information:

A rectangle ADCB and a square ASQU.

BC = AD = 9

CD = AB = 5

SQ = QU = UA = AS = 3.

Formula used :

  $\begin{array}{l}Probabilityofaevent=\frac{possiblenumberofoutcomes}{totalnumberofoutcomes}\\ \end{array}$

Calculation:

Area of rectangle = length x breadth = 9 x 5 = 45.

Area of square = side x side = 3 x 3 = 9.

  $\begin{array}{l}Probabilityofaevent=\frac{possiblenumberofoutcomes}{totalnumberofoutcomes}\\ \end{array}$

  $Probabilitythatchosen pointisinsquareSQUA=\frac{9}{45}=\frac{1}{5}$

b.

To determine

The probability that chosen point is not in square SQUA.

Answer to Problem 15PSC

The probability that chosen point is in square SQUA is $\frac{4}{5}$

Explanation of Solution

Given information:

A rectangle ADCB and a square ASQU.

BC = AD = 9

CD = AB = 5

SQ = QU = UA = AS = 3.

Formula used :

  $\begin{array}{l}Probabilityofaevent=\frac{possiblenumberofoutcomes}{totalnumberofoutcomes}\\ \end{array}$

Calculation :

Area of rectangle = length x breadth = 9 x 5 = 45.

Area of square = side x side = 3 x 3 = 9.

Remaining area = 45 − 9 = 36

  $\begin{array}{l}Probabilityofaevent=\frac{possiblenumberofoutcomes}{totalnumberofoutcomes}\\ \end{array}$

  $Probabilitythatchosen pointisnotinsquareSQUA=\frac{36}{45}=\frac{4}{5}$