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1. anonymous

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

2. anonymous

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.

3. anonymous

huh???

4. anonymous

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?

5. anonymous

6.5

6. anonymous

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?

7. anonymous

so 3.14*6.5?

8. anonymous

20.41

9. anonymous

Close, but remember that the radius is squared.

10. anonymous

132.67

11. anonymous

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

12. anonymous

so 33.17

13. anonymous

Correct. So the area of 4 circles would be?

14. anonymous

33.17*4=132.68

15. anonymous

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?

16. anonymous

how would it be set up?

17. anonymous

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?

18. anonymous

so 132.68+6.5?

19. anonymous

139.18

20. anonymous

$A_{total} = 169$ $A_{circles} = 132.68$ What is $A_{not\ circles}$

21. anonymous

36.32

22. anonymous

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

23. anonymous

36.32/169

24. anonymous

.2149112

25. anonymous

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.

26. anonymous

21.49%

27. anonymous

Yep.

28. anonymous

thank you

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