Geometry Unit 12 Probability Notes

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12.4 Geometric Probability

Example 1: Lengths and Geometric Probability Point Z is chosen at random on AD. Find the probability that Z is on AB.

Guided Practice 1: Length Probabilities Point R is chosen at random on LO. Find the probability that R is on MN.

Example 2: Halley’s Comet orbits Earth every 76 years. What is the probability that Halley’s Comet will complete an orbit within the next decade?

Example 2B: Translations in a Coordinate Plane SUBWAY You are in the underground station waiting for the next subway car, and are unsure how long ago the last one left. You do know that the subway comes every sixteen minutes. What is the probability that you will get picked up in the next 12 minutes?

Geometry Unit 12 Probability Notes

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Example 3: Area and Geometric Probability DARTS The targets of a dartboard are formed by 3 concentric circles. If the diameter of the center circle is 4 inches and the circles are spread 3 inches apart, what is the probability that a player will throw a dart into the center circle?

Guided Practice 3: RING TOSS If at a carnival, you toss a ring and it lands in the red circle shown below, then you win a prize. The diameter of the circle is 4 feet. If the dimensions of the blue table are 8 feet by 5 feet, what is the probability if the ring is thrown at random that you will win a prize?

Example 4: Angle Measure Probability Use the spinner to find the P (pointer landing on section 3). Use the spinner to find the P (pointer landing on section 1).

Guided Practice 4: Use the spinner to find the P (pointer landing on section C). Use the spinner to find the P (pointer landing on section E).

Geometry Unit 12 Probability Notes

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12.5 Probability and the Multiplication Rule

Independent Events: Dependent Events: Example 1: Determine whether the event is independent or dependent. Explain your reasoning. A. Anna rolls a 6 on one number cube and a 3 on another cube. B. A queen is selected from a standard deck of cards and not put back. Then a king is selected.

Guided Practice 1: Determine whether the event is independent or dependent. Explain your reasoning. A. A marble is selected from a bag. It is not put back. Then a second marble is selected. B. A marble is selected from a bag. Then a card is selected from a deck of cards.

Example 2: A bag contains a white marble, a blue marble, a yellow marble, and a green marble. Andrew selects the white marble, replaces it, and then selects the green marble.

Are these events independent? Explain using probability.

Geometry Unit 12 Probability Notes

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Guided Notes: EATING OUT Michelle and Christina are going out to lunch. They put 5 green slips of paper and 6 red slips of paper into a bag. If a person draws a green slip, she will order a hamburger. If she draws a red slip, she will order pizza. Michelle will draw first and put her slip back. Then Christina will draw. What is the probability that both girls draw green slips? Your Turn: LABS In Science class, students are drawing marbles out of a bag to determine lab groups. There are 4 red marbles, 6 green marbles, and 5 yellow marbles left in the bag. Jacinda draws a marble, but not liking the outcome, she puts it back and draws a second time. What is the probability that each of her 2 draws gives her a red marble?

Geometry Unit 12 Probability Notes

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GAMES At the school carnival, winners in the ringtoss game are randomly given a prize from a bag that contains 4 sunglasses, 6 hairbrushes, and 5 key chains. The first three players all win prizes. Find each probability. A. P (sunglasses, hairbrush, key chain) B. P (hairbrush, hairbrush, not a hairbrush) LABS In Science class, students are again drawing marbles out of a bag to determine lab groups. There are 4 red marbles, 6 green marbles, and 5 yellow marbles. This time Graham draws a marble and does not put his marble back in the bag. Then his friend Meena draws a marble. What is the probability they both draw green marbles? Davina’s family will cancel their weekend camping trip if the probability of rain on both Saturday and Sunday is greater than 10%. According to the weather forecast, there is a 30% chance of rain on Saturday and a 20% chance of rain on Sunday. Assuming the two events (rain on Saturday and rain on Sunday) are independent, should Davina’s family cancel the trip? Justify your answer using probability Find the probability of rain on Saturday and Sunday. Should Davina’s family cancel their weekend trip?