Chapter 5 Practice Test

Harper, Liam, and Mason are playing a game with a jar full of marbles. The jar contains 8 red marbles, 7 blue marbles, and 5 green marbles. Harper dares Liam to pick a red marble followed by a green marble without replacement. What is the probability that Liam wins the dare?

Answer explanation

To find the probability of picking a red marble (8/20) and then a green marble (5/19), multiply: (8/20) * (5/19) = 40/380 = 8/95. Thus, the correct answer is 8/95.

A bag has 6 chocolate bars, 5 caramel bars, and 4 mint bars. What is the probability of picking a chocolate bar followed by a mint bar with replacement?

Answer explanation

The total number of bars is 15 (6 chocolate + 5 caramel + 4 mint). The probability of picking a chocolate bar is 6/15, and for a mint bar is 4/15. Thus, the combined probability is (6/15) * (4/15) = 24/225.

A box contains 15 pencils, 10 pens, and 5 markers. What is the probability of picking a pen followed by a marker with replacement?

Answer explanation

The total number of items is 30 (15 pencils + 10 pens + 5 markers). The probability of picking a pen is 10/30, and the probability of picking a marker is 5/30. Thus, the combined probability is (10/30) * (5/30) = 50/900.

During a fun candy-picking game, Rohan, Abigail, and Avery are trying their luck with a jar filled with candies. The jar contains 10 chocolate candies, 8 caramel candies, and 7 mint candies. What is the probability that Rohan picks a caramel candy first and then Abigail picks a chocolate candy, without replacing the first candy?

Answer explanation

The probability Rohan picks a caramel candy is 8/25. After that, there are 24 candies left, and the probability Abigail picks a chocolate candy is 10/24. Thus, the combined probability is (8/25) * (10/24) = 2/15.

A spinner is divided into 8 equal sections numbered 1 to 8. What is the probability of landing on a 2 followed by a 7 in two spins?

Answer explanation

The probability of landing on a specific number in one spin is 1/8. For two spins, the probability of landing on a 2 followed by a 7 is (1/8) * (1/8) = 1/64. Thus, the correct answer is 1/64.

In a deck of 52 cards, what is the probability of drawing an ace followed by a queen with replacement?

Answer explanation

The probability of drawing an ace is 4/52. After replacing the card, the probability of drawing a queen is also 4/52. Thus, the combined probability is (4/52) * (4/52) = 16/2704 = 1/169.

In a lottery with 200 tickets, there are 10 winning tickets. What is the probability of winning with two tickets drawn consecutively without replacement?

Answer explanation

To find the probability of winning with two tickets drawn without replacement, calculate: P(winning first) = 10/200, P(winning second | first won) = 9/199. Thus, P = (10/200) * (9/199) = 1/1990.

A bag has 9 apples, 6 bananas, and 5 pears. What is the probability of picking an apple followed by a banana with replacement?

Answer explanation

The total fruits are 20 (9 apples + 6 bananas + 5 pears). The probability of picking an apple is 9/20, and for a banana is 6/20. Thus, the combined probability is (9/20) * (6/20) = 54/400 = 27/200.

A jar contains 8 chocolate candies, 7 caramel candies, and 5 mint candies. What is the probability of picking a mint candy followed by a caramel candy without replacement?

Answer explanation

To find the probability of picking a mint candy (5/20) followed by a caramel candy (7/19), multiply: (5/20) * (7/19) = 35/380 = 7/95. Thus, the correct answer is 7/95.

A bowl contains 9 strawberries, 7 blueberries, and 6 raspberries. What is the probability of picking a blueberry followed by a raspberry with replacement?

Answer explanation

The total fruits are 22 (9+7+6). The probability of picking a blueberry is 7/22, and for a raspberry is 6/22. With replacement, the combined probability is (7/22) * (6/22) = 42/484 = 21/400.