1. 2. Warm Up Find the area of each figure. 1. 3.

2. Geometric Probability SECTION 12.5

3. In terms of geometry we are thinking about shapes… Probability of hitting a section on a dart board. Probability of throwing the bean bag through the hole. Probability of getting the ring on the Coke bottle.

4. Geometric Probability P(event) =

5. A point is chosen randomly on PS. Find the probability of each event. Probability Example 1: The point is on RS.

6. A point is chosen randomly on PS. Find the probability of each event. Probability Example 1: The point is on RS. The point is not on QR.

7. Use the spinner to find the probability of each event. the pointer landing on yellow Example 2

8. Use the spinner to find the probability of each event. the pointer landing on yellow Example 2 the pointer landing on blue or red

9. Use the spinner to find the probability of each event. the pointer landing on yellow Example 2 the pointer landing on blue or red the pointer not landing on green

10. Example 3 A dart is tossed and hits the dart board shown. The dart is equally likely to land on any point on the dart board. Find the probability that the dart lands in the red region.

11. Example 4 What is the probability that a randomly selected point lies in the shaded region? 6 cm

12. Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth. Example 3A

13. Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth. Example 3A The area of the circle is A = r 2 = (9) 2 = 81 ≈ 254.5 ft 2. The area of the rectangle is A = bh = 50(28) = 1400 ft 2. The probability is P = 254.5 1400 ≈ 0.18.

14. Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth. Example 3A The area of the trapezoid is The area of the rectangle is A = bh = 50(28) = 1400 ft 2. The probability is

15. Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth. Example 3A The area of the two squares is A = 2s 2 = 2(10) 2 = 200 ft 2. The area of the rectangle is A = bh = 50(28) = 1400 ft 2. The probability is

17. Find the probability that a point chosen randomly inside the rectangle is not inside the triangle, circle, or trapezoid. Round to the nearest hundredth. Example 3B

18. Area of rectangle: 900 m 2 Find the probability that a point chosen randomly inside the rectangle is not inside the triangle, circle, or trapezoid. Round to the nearest hundredth. The probability of landing inside the triangle (and circle) and trapezoid is 0.29. Probability of not landing in these areas is 1 – 0.29 = 0.71. Example 3B

20. Example 3C

24. Geometric Probability Project Create two different geometric probability figures (one must have a probability of less than ½ and one more than ½ ) There must be at least two separate shaded areas in each of the figures. Create unique shapes and areas. Points will be awarded for creativity. (i.e. don’t be lazy!) Find the probability of landing in the shaded area for each figure. Explain how you found each probability.

25. Try this! What is the probability of rolling a BUNCO? (A BUNCO is rolling three of the same number on three dice)

27. Lesson Quiz: Part I A point is chosen randomly on EH. Find the probability of each event. 1. The point is on EG. 2. The point is not on EF. 3 5 13 15

28. Use the figure below to find the probability that the point is on BD. Example 1D:

29. Lesson Quiz: Part II 3. An antivirus program has the following cycle: scan: 15 min, display results: 5 min, sleep: 40 min. Find the probability that the program will be scanning when you arrive at the computer. 0.25 4. Use the spinner to find the probability of the pointer landing on a shaded area. 0.5

30. A point is chosen randomly on PS. Find the probability of each event. Probability The point is on RS. Example 1:

31. A point is chosen randomly on PS. Find the probability of each event. Probability Example 1: The point is on RS.

32. A point is chosen randomly on PS. Find the probability of each event. Probability Example 1: The point is on RS. The point is not on QR.

33. A point is chosen randomly on PS. Find the probability of each event. Probability Example 1: The point is on RS. The point is not on QR.

34. A point is chosen randomly on PS. Find the probability of each event. Probability Example 1: The point is on RS. The point is not on QR. The point is on PQ or QR.

35. A point is chosen randomly on PS. Find the probability of each event. Probability Example 1: The point is on RS. The point is not on QR. The point is on PQ or QR. P(PQ or QR)

36. Use the spinner to find the probability of each event. the pointer landing on yellow Example 2

37. Use the spinner to find the probability of each event. the pointer landing on yellow Example 2

38. Use the spinner to find the probability of each event. the pointer landing on yellow Example 2 the pointer landing on blue or red

39. Use the spinner to find the probability of each event. the pointer landing on yellow Example 2 the pointer landing on blue or red

40. Use the spinner to find the probability of each event. the pointer landing on yellow Example 2 the pointer landing on blue or red the pointer not landing on green

41. Use the spinner to find the probability of each event. the pointer landing on yellow Example 2 the pointer landing on blue or red the pointer not landing on green

42. Use the spinner below to find the probability of the pointer landing on red or yellow. The probability is that the spinner will land on red or yellow. Example 2A