Answer:
The sample space for selecting the group to test contains 2,300 elementary events.
Step-by-step explanation:
There are a total of N = 25 aluminum castings.
Of these 25 aluminum castings, n₁ = 4 castings are defective (D) and n₂ = 21 are good (G).
It is provided that a quality control inspector randomly selects three of the twenty-five castings without replacement to test.
In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.
The formula to compute the combinations of k items from n is given by the formula:
[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]
Compute the number of samples that are possible as follows:
[tex]{25\choose 3}=\frac{25!}{3!\times (25-3)!}[/tex]
[tex]=\frac{25\times 24\times 23\times 22!}{3!\times 22!}\\\\=\frac{25\times 24\times 23}{3\times 2\times 1}\\\\=2300[/tex]
The sample space for selecting the group to test contains 2,300 elementary events.
