Question 12, 11.7.41 $$ \leqslant \begin{array}{l} ext { AW Score: } 29.69 \% ext {, } \ ext { An ice chest contains six cans of apple juice, four cans of grape juice, seven cans of } \ ext { orange juice, and eight cans of mango juice. Suppose that you reach into the container and } \ ext { randomly select three cans in succession. Find the probability of selecting no apple juice. }\end{array} $$ The probability of selecting no apple juice from the ice chest is (Type an integer or a simplified fraction.)

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Question 12, 11.7.41 $$ \leqslant \begin{array}{l}	ext { AW Score: } 29.69 \% 	ext {, } \ 	ext { An ice chest contains six cans of apple juice, four cans of grape juice, seven cans of } \ 	ext { orange juice, and eight cans of mango juice. Suppose that you reach into the container and } \ 	ext { randomly select three cans in succession. Find the probability of selecting no apple juice. }\end{array} $$ The probability of selecting no apple juice from the ice chest is (Type an integer or a simplified fraction.)

UpStudy AI · Accepted Answer

We first determine the total number of cans and the number of non‐apple juice cans.

1. Total number of cans:
   $$
   6 \text{ (apple)} + 4 \text{ (grape)} + 7 \text{ (orange)} + 8 \text{ (mango)} = 25.
   $$

2. Number of non‐apple juice cans:
   $$
   25 - 6 = 19.
   $$

When selecting three cans in succession without replacement, the probability that none is apple juice is given by the ratio of the number of ways to choose three non‐apple cans to the number of ways to choose any three cans.

3. Compute the number of ways to choose three non‐apple cans:
   $$
   \binom{19}{3} = \frac{19 \times 18 \times 17}{3 \times 2 \times 1} = \frac{5814}{6} = 969.
   $$

4. Compute the total number of ways to choose any three cans:
   $$
   \binom{25}{3} = \frac{25 \times 24 \times 23}{3 \times 2 \times 1} = \frac{13800}{6} = 2300.
   $$

5. Therefore, the probability of selecting no apple juice is:
   $$
   \frac{\binom{19}{3}}{\binom{25}{3}} = \frac{969}{2300}.
   $$

The probability of selecting no apple juice from the ice chest is $$\frac{969}{2300}$$.
The probability of selecting no apple juice is $$\frac{969}{2300}$$.

Question 12, 11.7.41

The probability of selecting no apple juice from the ice chest is
(Type an integer or a simplified fraction.)

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Question 12, 11.7.41 The probability of selecting no apple juice from the ice chest is (Type an integer or a simplified fraction.)