An ice chest contains six cans of apple juice, eight cans of grape juice, four cans of
orange juice, and two cans of mango juice. Suppose that you reach into the container and
randomly select three cans in succession. Find the probability of selecting a can of orange
juice, then a can of mango juice, then a can of grape juice.
The probability of selecting from the ice chest a can of orange juice, then a can of mango
juice, then a can of grape juice is
(Type an integer or a simplified fraction.)

Question

UpStudy AI · Accepted Answer

1. There are a total of $$6 + 8 + 4 + 2 = 20$$ cans.

2. The probability that the first can selected is orange is 
$$
\frac{4}{20} = \frac{1}{5}.
$$

3. Once an orange can is removed, there are $$20 - 1 = 19$$ cans left. The probability that the second can selected is mango is 
$$
\frac{2}{19}.
$$

4. After removing both an orange and a mango can, there are $$19 - 1 = 18$$ cans remaining. The probability that the third can selected is grape is 
$$
\frac{8}{18} = \frac{4}{9}.
$$

5. The overall probability of selecting an orange can, then a mango can, then a grape can in succession is the product of the individual probabilities:
$$
\frac{1}{5} \times \frac{2}{19} \times \frac{4}{9} = \frac{8}{855}.
$$

Thus, the probability is 
$$
\boxed{\frac{8}{855}}.
$$
The probability of selecting an orange juice can first, then a mango juice can, and finally a grape juice can is $$\frac{8}{855}$$.

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