Question

an ice chest contains 6 cans of apple juice, 4 cans of grape juice, 7 cans of orange juice, and 5 cans of mango juice. suppose that you reach into the container and randomly select three cans in succession. find the probability of selecting three cans of apple juice. the probability of selecting from the ice chest three cans of apple juice is \boxed{}. (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate the total number of cans

The total number of cans is \(6 + 4+7 + 5=22\) cans.

Step2: Calculate the probability of selecting the first can of apple juice

The probability of selecting the first can of apple juice is \(\frac{6}{22}\).

Step3: Calculate the probability of selecting the second can of apple juice

After selecting one can of apple juice, there are \(22 - 1=21\) cans left and \(6- 1 = 5\) cans of apple juice left. So the probability is \(\frac{5}{21}\).

Step4: Calculate the probability of selecting the third can of apple juice

After selecting two cans of apple juice, there are \(21-1 = 20\) cans left and \(5 - 1=4\) cans of apple juice left. So the probability is \(\frac{4}{20}\).

Step5: Calculate the combined probability

Since these are independent - sequential events, we multiply the probabilities together. \(P=\frac{6}{22}\times\frac{5}{21}\times\frac{4}{20}\)

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Answer:

\(\frac{1}{77}\)