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§10.6, Geometric Probability

§10.6, Geometric Probability. Learning Targets. I will calculate geometric probabilities. I will use geometric probability to predict results in real-world situations. Vocabulary. geometric probability.

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§10.6, Geometric Probability

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  1. §10.6, Geometric Probability Learning Targets I will calculate geometric probabilities. I will use geometric probability to predict results in real-world situations. Vocabulary geometric probability

  2. Remember that in probability, the set of all possible outcomes of an experiment is called the sample space. Any set of outcomes is called an event. If every outcome in the sample space is equally likely, the theoretical probability of an event is Geometric probability is used when an experiment has an infinite number of outcomes. In geometric probability, the probability of an event is based on a ratio of geometric measures such as length or area. The outcomes of an experiment may be points on a segment or in a plane figure.

  3. 10-6

  4. The point is on RS. The point is on QS. A point is chosen randomly on PS. Find the probability of each event. The point is not on QR. The point is not on RS. 10-6

  5. Use the figure below to find the probability that the point is on BD. 10-6

  6. A pedestrian signal at a crosswalk has the following cycle: “WALK” for 45 seconds and “DON’T WALK” for 70 seconds. What is the probability the signal will show “WALK” when you arrive? To find the probability, draw a segment to represent the number of seconds that each signal is on. 45 70 0 45 115 The signal is “WALK” for 45 out of every 115 seconds. 10-6

  7. If you arrive at the light 40 times, you will probably stop and wait more than 40 seconds about (40) ≈ 10 times. If you arrive at the signal 40 times, predict about how many times you will have to stop and wait more than 40 seconds. In the model, the event of stopping and waiting more than 40 seconds is represented by a segment that starts at B and ends 40 units from C. The probability of stopping and waiting more than 40 seconds is 0 30 70 0 B C 115

  8. A traffic light is green for 25 seconds, yellow for 5 seconds and red for 30 seconds. When you arrive at the light was is the probability that it is green? 10-6

  9. Use the spinner to find the probability of the pointer landing on yellow. The angle measure in the yellow region is 140°. the pointer landing on blue or red the pointer not landing on green 10-6

  10. ≈ 0.18. The probability is P = 254.5 1400 Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth. the circle The area of the circle is A = r2 = (9)2 =81 ≈ 254.5 ft2. The area of the rectangle is A = bh = 50(28)=1400 ft2. 10-6

  11. The area of the trapezoid is The probability is the trapezoid The area of the rectangle is A = bh = 50(28)=1400 ft2. 10-6

  12. The probability is one of the two squares The area of the two squares is A = 2s2 = 2(10)2 =200 ft2. The area of the rectangle is A = bh = 50(28)=1400 ft2. 10-6

  13. EXIT CHECK 13 3 15 5 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. 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 10-6

  14. EXIT CHECK 4. Use the spinner to find the probability of the pointer landing on a shaded area. 0.5 5. Find the probability that a point chosen randomly inside the rectangle is in the triangle. 0.25

  15. HOMEWORK: Page 721, #18 – 24, 27, 28, 38

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