A bag contains 9 red marbles, 4 blue marbles, and 7 yellow marbles. You randomly select three marbles from the bag. a. What is the probability that all three marbles are red when you replace each marble before selecting the next marble? Round your answer to the nearest tenth. about % b. What is the probability that all three marbles are red when you do not replace each marble before selecting the next marble? Round your answer to the nearest tenth. about %

Question

Madilynn

Mathematics

17 January, 08:29

A bag contains 9 red marbles, 4 blue marbles, and 7 yellow marbles. You randomly select three marbles from the bag. a. What is the probability that all three marbles are red when you replace each marble before selecting the next marble? Round your answer to the nearest tenth. about % b. What is the probability that all three marbles are red when you do not replace each marble before selecting the next marble? Round your answer to the nearest tenth. about %

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Answers (1)

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Cristofer · Answer 1

Answer: 9.1 % and 7.4 %

Step-by-step explanation:

A)

There are a total of 9 + 4 + 7 = 20

The probability that you select a red marble is 9/20.

Since we are constantly replacing the marble, the probability is always the same

Hence, the probability is (9/20) ^3=.091125

Converting this to a percent, this is around 9.1 percent.

B)

As previously stated, the probability that you select a red marble is 9/20. However, after we select the first one, the amount decreases by 1, and the amount of red marbles decreases by 1.

So our probability is 9/20 * 8/19 * 7/18 = 7/95, which is approximately 7.4 percent.