Question

a dart hits the dartboard shown find the probability that it lands in the shaded regions? I don't know how to do this help

Answer 1

The probabiity of a dart landing on the shaded regions is 0.2125

Here, we want to find the probability that the dartboard hits the shaded regions

Mathematicaly, all we have to do is to calculate the portion of the board that is shaded

All we have to do is to subtract the area of the 4 circles from the area of the given square

Area of the square is the square of its side

We have this as;

`\text{Area of square = 4}*4=16m^2`

The circles are similar

Thus, their areas are same

We only need to calculate the area of one of the circles and multiply by four

As we can see, 4 m represents the diameters of two circles combined

The diameter of one of the circles will thus be 2 m

The radius we will need in the calculations is half of this

We have the radius as 2/2 = 1 m

The area of the circles is thus;

`4*\pi* r^2\text{ = 4}*3.142\text{ }*1^2=12.6m^2`

The area of the shaded part is thus;

`16-12.6=3.4m^2`

So, the probability of the dart hitting the shaded portion will be;

`(3.4)/(16)\text{ = 0.2125}`