An ice chest contains 6 cans of apple juice, 4 cans of grape juice, 5 cans of orange juice, and 8 cans of mango juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting no grape juice.

Question

Alice Drake

Mathematics

19 October, 16:38

An ice chest contains 6 cans of apple juice, 4 cans of grape juice, 5 cans of orange juice, and 8 cans of mango juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting no grape juice.

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Answers (1)

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Frances Spears · Answer 1

(19/23) (18/22) (17/21) or 969/1771

Step-by-step explanation:

You add up the total number of cans, giving you 6+4+5+8 = 23 cans total. From there, you only have 4 cans of grape juice. That means 19 of these cans aren't grape, meaning you are checking the probability of choosing these three times in a row.

The probability of selecting the first can and it not being grape is 19/23. Then, when you select another can in succession, without replacing the cans, you now only have 22 cans left, meaning 18 also will not be grape, so it will be a 18/22 chance. Then, selecting your third can, 21 cans are left, and 17 of them are not grape since you have not yet chosen one, giving you 17/21. You multiply them together.

Hopefully I reduced the fraction properly (or even did this question properly)