Question

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Explanation:

Step1: Recall Independent Events Rule

For two events \( A \) and \( B \), they are independent if \( P(A \cap B)=P(A)\cdot P(B) \). Here, \( A \) is red, \( B \) is green.

Step2: Calculate \( P(\text{red})\cdot P(\text{green}) \)

\( P(\text{red})=\frac{1}{2} \), \( P(\text{green})=\frac{1}{4} \). So \( P(\text{red})\cdot P(\text{green})=\frac{1}{2}\times\frac{1}{4}=\frac{1}{8} \).

Step3: Compare with \( P(\text{red and green}) \)

Given \( P(\text{red and green})=\frac{1}{8} \), so \( P(\text{red})\cdot P(\text{green}) = P(\text{red and green}) \). Thus events are independent.

Answer:

The events are independent because \( P(\text{red}) \cdot P(\text{green}) = P(\text{red and green}) \). (The first option)