probability based on area

Question

Answer 1

When working on a problem like this one, think about the following formula

P(Event) = (Number of ways the event can occur) / (Total number of possible outcomes)

In this case, we are looking at an area of a rectangle, let's start by finding the total area, i.e. the Total number of possible outcomes.

Total Area = Length x Width = (10+20) x (8+12) = 30 x 20 = 600

Now we can find the area of the rectangle labeled A, i.e. the Number of ways the event can occur,

Area of A = 8 x 20 = 160

Now we can find our probability by plugging these numbers into the above formula,

P(random point in A) = 160 / 600 = 16 / 60 = 4 / 15

So the probability of a random point being in the rectangle A is 4 / 15.

To convert this to a percentage. plug this faction into a calculator to receive the decimal 0.26666....

Then multiply by 100,

100x(0.26666....) = 26.67% [Rounding to the nearest hundredth]

Answer 2

The dimensions of the entire figure are 20 by 30. The area of the entire figure is 20*30 = 600

The dimensions of section A are 20 by 8. The area of section A is 20 * 8 = 160

The probability of a point being in section A is ratio of area in section A/area of entire figure * 100 %