Explanation:
We can solve this problem using the hypergeometric distribution.
The total number of apples is 24 (4 bad + 20 good). Let X be the number of bad apples in a draw of 2 apples.
The probability of drawing 0 bad apples is:
P(X=0) = (20 choose 2) / (24 choose 2) = 190 / 276
The probability of drawing 1 bad apple is:
P(X=1) = ((4 choose 1) * (20 choose 1)) / (24 choose 2) = 64 / 276
The probability of drawing 2 bad apples is:
P(X=2) = (4 choose 2) / (24 choose 2) = 1 / 276
Therefore, the probability distribution of the number of bad apples in a draw of 2 apples at random is:
X | 0 | 1 | 2
----|------|------|-----
P(X) |190/276|64/276|1/276