Probability, permutations and combinations

Probability, permutations and combinations

Multiple Choice

1. A rectangular piece of stained glass has the dimensions shown in the diagram. What is the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid?

• $\frac{1}{3}$

• $\frac{4}{9}$

• $\frac{5}{9}$

• $\frac{2}{3}$

Multiple Choice

2. There are 5 red tiles and 5 blue tiles with the letter A in a bag. There are also 6 red tiles and 4 blue tiles with the letter B in the bag. What is the probability that a randomly selected tile is blue or has the letter B?

• $\frac{9}{20}$

• $\frac{1}{2}$

• $\frac{3}{4}$

• $\frac{19}{20}$

Multiple Select

3. Which of the following pairs of events are independent? Select ALL that apply.

• Draw a 2 of clubs from a standard deck of 52 cards, keep it, and then draw a 2 of diamonds

• Draw a 3 of spades from a standard deck of 52 cards, replace it, and then draw a 5 of hearts

• Roll a number cube. Then roll again if the first roll is a 6

• Events A and B, where P(A) = 0.1, P(B) = 0.5, and P(A and B) = 0.05

• Events A and B, where P(A) = 0.4, P(B) = 0.2, and P(A and B) = 0.8

Fill in the Blanks

4. On a track and field team, 8% of the members run only long-distance, 32% compete only in field events, and 12% are sprinters only. Find the probability that a randomly chosen team member runs only long-distance or competes only in field events. Express your answer as a decimal.

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5a. The probability that Shaq will make a free throw is 30%. The probability that he will make two consecutive free throws is...(type in your answer as a decimal)

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5b. The probability that Shaq makes a free throw is 30%. The probability that he will make the first and not the second is...

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5c. The probability that Shaq makes a free throw is 30%. The probability that he will not make either of two free throws is...

Multiple Choice

6. A bookstore classifies its books by reader group, type of book, and cost. What is the probability that a book selected at random is a child's book, given that it costs $15?

• $\frac{315}{1005}$

• $\frac{470}{1005}$

• $\frac{315}{575}$

• $\frac{470}{575}$

Multiple Choice

7. Half of a class took Form A of a test and half took Form B. Of the students who took form B, 39% passed. What is the probability that a randomly chosen student took Form B and did not pass?

• 0.055

• 0.195

• 0.305

• 0.390

Multiple Select

8. Which of the following are true if events A and B are independent?

• P(A | B) = P(A)

• P(A | B) = P(B)

• P(A | B) = P(A and B)

• P(B | A) = P(A)

• P(B | A) = P(B)

Fill in the Blanks

9. Three-fourths of a research team worked in a lab while one-fourth of the team worked near a pond. Of the researchers who worked near the pond, 14% collected insects. What is the probability that a randomly chosen researcher worked near the pond and collected insects? Type your answer as a decimal.

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10a. A bag contains 4 blue and 6 green marbles. Two marbles are selected at random from the bag. If the first marble is replaced before the second marble is drawn, what is P(blue second | green first)? Express your answer as a fraction (a/b)

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10b. A bag contains 4 blue and 6 green marbles. Two marbles are selected at random from the bag. If the first marble is not replaced before the second marble is drawn, what is P(blue second | green first)? Express your answer as a fraction (a/b)

Multiple Choice

11. A chef randomly chooses 5 apples from a case of 24 apples. Which best represents the number of ways the chef can make the selection?

• $_5C_{19}$

• $_{24}C_5$

• $_5C_{24}$

• $_{19}P_5$

Multiple Choice

12. A game at the fair involves balls numbered 1 to 18. You can win a prize if you correctly choose the 5 numbers that are randomly drawn. What is your approximate chance of winning?

• 0.0001 or 0.01%

• 0.056 or 5.6%

• 0.078 or 7.8%

• 0.278 or 27.8%

Multiple Select

13. Select ALL the permutations.

• 6 books are placed from left to right on a bookshelf

• 4 goldfish are selected from a tank containing 8 goldfish

• 3 class representatives are chosen from 25 students

• Co-captains are named from a team of 16 players

• Each number 1 to 5 is used to make a 5-number security code

Fill in the Blanks

14. A bag contains 7 marbles: one each of red, orange, yellow, green, blue, violet, and white. A child randomly pulls 4 marbles from the bag. What is the probability that the marbles chosen are green, blue, red, and yellow? Round your answer to the nearest hundredth.

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15a. Serena has a playlist of 10 songs. She plays 2 songs. The probability that she hears her 2 favorite songs can be found using a number of combinations and is...(express your answer as a fraction a/b)

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15b. Serena has a playlist of 10 songs. She plays 2 songs. The probability that she hears her favorite song first and her next favorite song second can be found using a number of permutations and is...(express your answer as a fraction a/b)