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Pre-AP Geometry – Chapter 14 Test Review Standards/Goals:

A.1.f.: I can find the probability of a simple event.

F.1.c.: I can use area to solve problems involving geometric probability.

S.CP.1: I can define the union, intersection and complements of events in the context of probability.

S.CP.2.: I can determine if two events are independent or not.

S.CP.3.: I can determine the independence of two events based on a conditional probability.

S.CP.4.: I can use a two-way table involving categories to determine probabilities.

S.CP.5.: I can recognize the concepts of conditional probabilities and independence in everyday situations.

S.CP.6.: I can calculate a conditional probability and interpret the result in the context of the given problem.

S.CP.7.: I can use the General Addition rule for both mutually exclusive and non-mutually exclusive events.

S.CP.8(+): I can use the General Multiplication rule for events that are not independent.

S.CP.9 (+): I can use combinations and permutations to compute probabilities.

S.MD.6(+): I can compute both experimental and theoretical probabilities.

#1. What is the probability of rolling a number that fits the following criteria?

a. Greater than 2 on a number cube?

b. Greater than or equal to 2 on a number cube?

c. Less than 6 on a number cube?

d. Less than or equal to 3 on a number cube?

e. Greater than 4 on a number cube?

#2. A coin is tossed 40 times and lands on heads 21 times. What is the experimental probability of the coin landing on tails? #3. What is the theoretical probability of randomly choosing a history book from a shelf that holds 6 romance novels, 9 history books, and 4 sports books? #4. What is the complement of rolling a 1 or 3 on a number cube?

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#5. Point X is chosen at random on 𝐿𝑃̅̅̅̅ . Find the probability of each event. a. P(X is on LN)

b. P(X is on MO) #6. Find the number of possible outcomes for creating an outfit from 4 pairs of pants, 3 skirts, 3 shirts, and 6 pairs of shoes.

Use the following to answer the next FOUR questions: Goals 0 1 2 3

Frequency 5 8 7 2

#7. How many games did the team play? #8. What is the relative frequency of games with 1 goal scored? #9. What is the probability that the team scored 2 or more goals? #10. Which expression can be used to determine the probability of scoring fewer than 3 goals? #11. What is the probability of rolling a 3 or 4 on a number cube and randomly drawing the 4 of spades from a deck of cards? #12. In one class, 25% of the students received an A on the last test and 33% of the students received a B. What is the probability that a randomly chosen student received an A or a B? #13. What is the probability of rolling a 3 or a number less than 5 on a number cube? #14. You win 4 out of every 10 races that you run. Your friend wins 5 out of every 9 swimming competitions she enters. What is the probability of you both winning the next events? #15. What is the probability of rolling TWO 1’s if you roll a pair of dice? #16. What is the probability of drawing a KING or a DIAMOND from a standard deck of cards? #17. What is the probability of rolling a pair of dice and NOT rolling a 2 or a 3?

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#18. Find the probability of a point chosen at random being in the NON-shaded area of the diagram shown. The table below shows the number of participants at a charity event who walked or ran, and who wore a red t-shirt or a blue t-shirt. Use the table for the next FOUR QUESTIONS:

BLUE T-shirt RED T-shirt TOTALS

Walk 60 50 110 Run 35 25 60

Totals 95 75 170

#19. What is the probability that a randomly chosen person ran AND wore a red t-shirt? #20. What is the probability that a randomly chosen person walked AND wore a blue t-shirt? #21. What is the P(walked ⎸ wore a red t-shirt)? #22. What is the probability that a randomly chosen walker wore a red t-shirt? #23. In how many different ways can 10 books be arranged on a bookshelf? #24. Three frogs are sitting on a 15 foot log. The first two are spaced 5 feet apart and the third frog is 10 feet away from the second one. What is the probability that when a fourth frog hops onto the log that it lands between the first two?

#25. Evaluate 𝑷𝒓𝒏 =𝒏!

(𝒏 −𝒓)! for n = 13 and r = 8.

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#26. The dance team is made up of 18 girls. A captain and TWO co-captains are selected at random. What is the probability that Sarah, Megan, and Ta’Nesha are chosen as leaders? #27. Mark has 12 baseball trophies but he only has room to display 7 of them. If he chooses them at random, what is the probability that each of the trophies from the school invitational from the 1st through 7th grades will be chosen? #28. The diagram shows the top of a student’s desk at home. A dart is dropped on the desk. What is the probability that the dart lands on the book report? #29. Use the spinner to find each probability. If the spinner lands on a line, it is spun again.

a. P(pointer landing on yellow)

b. P(pointer landing on orange)

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#30. As part of a promotion, a hockey team gives each fan entering the stadium one of 4 different randomly-chosen medallions. Using the random number table below, how many fans receive medallions before all 4 types are given out?

11232 32311 32431 42412 #31. Evaluate: 6! #32. Evaluate: #33. On a softball team, 30% of the players are chosen to play outfield. Of those chosen, 15% play center field. What is the probability that a student chosen to play outfield plays center field? #34. Events A and B are independent events. What is P(A and B) when P(A) = 50% and P(B) = 40%? #35. A box contains 6 red cubes, 3 green cubes, 4 red cubes, and 8 green balls. What is P(cube ⎸red)? #36. If a dart lands at random on the poster at the right, what is the probability that the dart will land inside one the polygons?

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#37. If a dart lands at random on the poster at the right, what

is the probability that the dart will land in a circle?

#38. ERROR ANALYSIS:

#39. Jordan has 9 blue balls, 6 red balls, and 5 brown balls in a box. Two balls are drawn without replacement from the box. What is the probability that both of the balls are brown? #40. Bella has 7 green beads, 10 yellow beads and 3 white beads in a pouch. Two beads are drawn without replacement from the pouch. What is the probability that both of the beads are yellow? #41. Evan has 4 pairs of black shoes and 4 pairs of brown shoes on his shoe rack. He picks one pair of shoes, records its color, puts it back on the rack. He then draws another shoe. What is the probability of taking out a black shoe followed by the brown shoe? #42. Caleb has 7 black caps, 4 yellow caps, and 9 blue caps in his wardrobe. Two caps are drawn without replacement from the wardrobe. What is the probability that both of the caps are blue?

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#43. In a trivia game, you answer correctly on 26% of the 5-point bonus questions, and you answer correctly on 68% of the 2-point questions. Find the expected values and compare them using <, >, or =. #44. In a carnival game, contestants can throw at 2 targets to win prizes. There is a 12% success rate of hitting target A, which yields a $7 prize. There is a 48% success rate of hitting target B, which yields a $3 prize. Compare the expected values using < ,>, or =. #45. A board game uses a spinner with equal-sized sections numbered 1, 2, 3, 4, 5, 6, and 7. Spinning an even number enables a player to move 2 spaces forward. Spinning an odd number makes a player move 1 space backward. What is the expected value, in fraction form, of each spin? #46. The cycle of the light on George Street at the intersection of George Street and Main Street is 10 seconds green, 5 seconds yellow, and 60 seconds red. If you reach the intersection at a random time, what is the probability that the light is red?

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PRACTICE MULTIPLE CHOICE QUESTIONS:

#1. Point X is chosen at random on 𝐽𝑀̅̅ ̅̅ . Find the probability that X is on 𝐾𝑀̅̅ ̅̅ ̅. a. 0.29 b. 0.4 c. 0.47 d. 0.79 e. None of the above.

#2. Using the table below, which numbers would you use to choose 3 students from a group of 50 students?

36674 86790 98265 42947 20763 a. 36, 48, 42 b. 36, 48, 26 c. 36, 48, 9 d. 48, 26, 42

#3. What is the probability of rolling TWO 6’s if you roll a pair of dice? a. 1/6 b. 1/36 c. 1/3 d. 1/18 e. None of the above

#4. What is the probability of rolling a pair of dice and NOT rolling a 6? a. 5/6 b. 1/6 c. 25/36 d. 1/36 e. None of the above

#5. In a game at the fair, a player has a 43% chance of making a 3 point shot and a 32% chance of making a 4 point shot. Which shows the greater probability shot and difference between expected values?

a. 4 point by 0.01 b. 4 point by 0.08 c. 3 point by 0.01 d. 3 point by 0.08

#6. Find the probability of point chosen at random being in the shaded area of the diagram shown.

a. 4/9 b. ¼ c. 1/9 d. ½ e. None of the above

#7.