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Transcript

Geometric Probability 5.8 • Calculate geometric probabilities. • Use geometric probability to predict results in real-world situations. Probability is the likelihood that an event will happen.. If every outcome in the sample space is equally likely, the theoretical probability of an event is Geometric Probability is probability with length or area. Use the Spinner to find the Probability The pointer landing on yellow. The angle measure in the yellow region is 140°. Use the Spinner to find the Probability The pointer landing on blue or red. The angle measure in the blue region is 52°. The angle measure in the red region is 60°. Use the Spinner to find the Probability The pointer not landing on green. The angle measure in the green region is 108°. Subtract this angle measure from 360°. Use the Spinner to find the Probability The pointer landing on red or yellow. The probability is that the spinner will land on red or yellow. Using Length to Find Geometric Probability A point is chosen randomly on PS. Find the probability of each event. The point is on RS. The point is not on QR. The point is on PQ or QR. P(PQ or QR) = P(PQ) + P(QR) Using Length to Find Geometric Probability Use the figure below to find the probability that the point is on BD. Using Length to Find Geometric Probability A point is chosen randomly on EH. Find the probability of each event. a. The point is on EG. 3 5 b. The point is not on EF. 13 15 Using Length to Find Geometric Probability 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. Walk Don’t Walk 45 sec. 70 sec. The signal is “WALK” for 45 out of every 115 seconds. Using Length to Find Geometric Probability A traffic light is green for 25 seconds, yellow for 5 seconds, and red for 30 seconds. What is the probability that the light will not be on red when you arrive? The probability that the light will not be on red is Using Length to Find Geometric Probability You are visiting San Francisco and are taking a trolley ride to a store on Market Street. You are supposed to meet a friend at a store at 3:00 PM The trolley runs every 10 minutes and the trip to the store is 8 minutes. You arrive at the trolley stop at 2:48 PM. What is the probability that you will arrive at the store by 3:00 PM? To begin find the greatest amount of time you can afford to wait for the trolley and still get to the store by 3 PM. Because the ride takes 8 minutes, you need to catch the trolley no later than 8 minutes before 3PM, or by 2:52 PM. Using Area to Find Geometric Probability If a dart hits the board below, find the probability that it will land in the shaded region. Divide into equal parts. 2 1 8 4 Using Area to Find Geometric Probability If a dart hits the board below, find the probability that it will land in the shaded region. 1 3 Using Area to Find Geometric Probability A square game board consists of shaded and non-shaded regions of equal width as shown. What is the chance that a dart thrown at the board will land in a shaded area? 72 P(event) 121 Using Area to Find Geometric Probability A regular hexagon is inscribed in a circle with a diameter of 12. Find the probability that a point chosen at random lies in the shaded regions. (Ao – A) 2 Ao (r2 – ½aP) 2 r2 36 36 12 3 3 6 18 – 27 3 36 P.086 or 8.6% Using Area to Find Geometric Probability A game board consists of a circle inscribed in a square. What is the chance that a dart thrown at the board will land in the shaded area? A – Ao A s2 – r2 s2 122 – 36 122 144 – 36 144 12 P .214 or 21.4% Using Area to Find Geometric Probability If a dart hits the board below, find the probability that it will land in the shaded region. A – 6Ao A lw – 6r2 lw 16 24 – 6 16 16 24 384 – 96 384 16 P .214 or 21.4% Using Area to Find Geometric Probability Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth. 2A P(A)= A 200 .14 P(A)= 1400 A A P(A)= P(A )= A A 81 .18 450 P(A)= .32 P(A )= 1400 1400 Using Area to Find Geometric Probability Find the probability that a point chosen randomly inside the rectangle is not inside the circle or trapezoid. Round to the nearest hundredth. A – Ao – A A 900 – 113.1 – 75 900 P .79 or 79% Using Area to Find Geometric Probability If a dart hits the board below, find the probability that it will land in the shaded region. A – A A S2 – s2 S2 52 – 32 52 25 – 9 25 P= .64 or 64% Using Area to Find Geometric Probability If a dart hits the board below, find the probability that it will land in the shaded region. A – Ao A R2 – r2 R2 9 – 4 9 5 9 5 9 P .556 or 55.6% a. 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 b. Use the spinner to find the probability of the pointer landing on a shaded area. 0.5 Find the probability that a point chosen randomly inside the rectangle is in the triangle. 0.25 0.087 0.196 0.4 0.67 0.67 A Sunday night sports show is on from 10:00 p.m. to 10:30 p.m. You want to find out if your favorite team won this weekend, but forgot that the show was on. You turn it on at 10:14 p.m. The score will be announced at one random time during the show. What is the probability that you haven’t missed the report about your favorite team? 0.53 0.6 0.47 0.5 0.07 0.82 0.33 1.00 Assignment Geometric Probability