An experiement has 10 equally likely outcomes. Let \( A \) and \( B \) be two non-empty events of the experiment. If \( A \) consists of 4 outcomes, the number of outcomes that \( B \) must have so that \( A \) and \( B \) are independent, is:
A and B are independent when \(P(A \cap B) = P(A)\,P(B)\).
Let B have \(b\) outcomes and \(A \cap B\) have \(k\) outcomes:
\(\frac{k}{10} = \frac{4}{10} \times \frac{b}{10} \Rightarrow k = \frac{4b}{10} = \frac{2b}{5}\)
\(k\) must be a whole number, so \(b\) must be a multiple of 5: \(b = 5\) (then \(k = 2\)) or \(b = 10\) (then \(k = 4\)).
Answer: (D) 5 or 10
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