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To determine if being left-handed is independent of gender, we can use the rule of independence in probability:

Two events, A and B, are independent if:

\[
P(A \cap B) = P(A) \times P(B)
\]

Where:
- \(P(A \cap B)\) is the probability of being both female and left-handed.
- \(P(A)\) is the probability of being female.
- \(P(B)\) is the probability of being left-handed.

From the question:
- \(P(\text{left-handed}) = 8\% = 0.08\)
- \(P(\text{female}) = 53\% = 0.53\)
- \(P(\text{female and left-handed}) = 4.24\% = 0.0424\)

Now, let's check if \(P(\text{female and left-handed})\) equals \(P(\text{female}) \times P(\text{left-handed})\).

Calculate \(P(\text{female}) \times P(\text{left-handed})\):

\[
0.53 \times 0.08 = 0.0424
\]

Since \(P(\text{female and left-handed}) = P(\text{female}) \times P(\text{left-handed})\), the two events are independent.

So, the correct answer is **Yes**. The events are independent.

Would you like more details or further clarification? Here are some related questions to explore:

1. How is the rule of independence in probability applied in real-life scenarios?
2. What are other methods to determine independence of events?
3. Can you explain dependent and independent events in probability theory?
4. How do we compute conditional probabilities?
5. What are some practical examples of mutually exclusive events?

**Tip:** Independence in probability means the outcome of one event does not affect the outcome of another.

Determine independence. According to a survey, 8% of students at a college are left-handed, 53% are female, and 4.24% are both female and left-handed. Is being left-handed independent of gender?

Learn how to determine whether left-handedness and gender are independent events using probability theory. This problem explores key concepts like event independence, conditional probabilities, and includes a step-by-step application of the rule of independence. Suitable for high school students.

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