Question

Find the probability that a randomly chosen point is located within the shaded region. Write your answer as a decimal, and

round to the nearest thousandth, if necessary.
6
3
Probability

Answer 1

`Probability = 0.25`

Explanation:

Given

The attached shape

Required

Probability of locating within the shaded region

First, calculated the area of the shaded region

`A_1 = 0.5 * base * height`

Where

`base = 8cm\\ height = 6cm` --- given

So:

`A_1 = 0.5 * 8cm* 6cm`

`A_1 = 24cm^2`

Next, calculated the area of the complete rectangle

`A_2 = Length* Width`

Where

`Width = 12cm\\ Length = 8cm` --- given

So:

`A_2 = 12cm * 8cm`

`A_2 = 96cm^2`

The required probability is:

`Probability = (A_1)/(A_2)`

`Probability = (24cm^2)/(96cm^2)`

`Probability = 0.25`