Question

Testing for spoiled wine. Suppose that you are purchasing cases of wine (12 bottles per case) and that, periodically, you select a test case to determine the adequacy of the bottles’ seals. To do this, you randomly select and test 3 bottles in the case. If a case contains 1 spoiled bottle of wine, what is the probability that this bottle will turn up in your sample?

Short answer

The probability that the spoiled bottle will turn up in the sample is 0.25.

Step-by-step solution

Given information

In a purchase case containing 12 bottles, randomly 3 bottles are selected.

Calculating the Probability 

Let X be the spoiled bottles in the sample.

Here, a case containing 1 spoiled bottle is taken.

By definitions, the probability that the spoiled bottle will turn up in the sample is given as

$\begin{array}{c}p=\frac{\left(\begin{array}{c}3\\ 1\end{array}\right)}{\left(\begin{array}{c}12\\ 1\end{array}\right)}\\ =\frac{3}{5}\\ =0.25\end{array}$

Hence, the probability that the spoiled bottle will turn up in the sample is 0.25.