Question

Please Help

Answer 1

Find the probability that a randomly chosen point in the figure lies in the shaded region...

Answer 2

What is the area of the whole square? What is the area of one of the circles? What is 4 times the area of one circle? What is the area of the whole square minus 4 times the area of one circle?

The answer to these questions should provide some insight into the solution. If you have questions or problems about how these areas are related post back and I can try to clarify.

Answer 3

huh???

Answer 4

What is the area of the entire square? Area of a rectangle = length * width. The length is 13, and the width is also 13. Therefore the area is 13*13 = 169. So assuming that each circle has a diameter of 1/2 of 13, what is the area of one of the circles?

Answer 5

6.5

Answer 6

6.5 would be the diameter. Half of that would be the radius.
\[ A_{Circle} = \pi r^2\]
Where r is the radius of the circle.
So what is the area of one circle?

Answer 7

so 3.14*6.5?

Answer 8

20.41

Answer 9

Close, but remember that the radius is squared.

Answer 10

132.67

Answer 11

Also recall that 6.5 is the diameter, not the radius. The radius is half the diameter or 3.25.

Answer 12

so 33.17

Answer 13

Correct. So the area of 4 circles would be?

Answer 14

33.17*4=132.68

Answer 15

Correct. So the probability of not being in any circles, is the area of the part of the square not in the circles, divided by the total area of the square.

If the total area of the square is 169, and the area of all the circles together is 132.68, what is the area of the portion of the square outside the circles?

Answer 16

how would it be set up?

Answer 17

Which? The area of the non-circle part?

\[A_{total} = A_{circles} + A_{not\ circles}\]

We have calculated the total Area, and the circular areas, so what is the non-circular area?

Answer 18

so 132.68+6.5?

Answer 19

139.18

Answer 20

\[A_{total} = 169\]
\[A_{circles} = 132.68\]

What is

\[A_{not\ circles}\]

Answer 21

36.32

Answer 22

Indeed. Now divide that area by the total area to find the probability for a random point to be in that area.

Answer 23

36.32/169

Answer 24

.2149112

Answer 25

Yep. Remember that probability of a situation is the number of ways that situation can occur divided by the total possible situations you can have. In this case we're working with areas, in the other example we were using lengths, but the process is the same.

Answer 26

21.49%

Answer 27

Yep.

Answer 28

thank you