To determine the probability \( P(A \text{ and } B) \) that would prove events \( A \) and \( B \) are independent, we can use the definition of independent events:
Two events \( A \) and \( B \) are independent if: \[ P(A \text{ and } B) = P(A) \times P(B) \]
Given:
- \( P(A) = 0.51 \) (or 51%)
- \( P(B) = 0.65 \) (or 65%)
Calculating \( P(A) \times P(B) \): \[ P(A \text{ and } B) = P(A) \times P(B) = 0.51 \times 0.65 \]
Calculating that: \[ 0.51 \times 0.65 = 0.3315 \] Converting this to a percentage: \[ 0.3315 = 33.15% \]
Now rounding to two decimal places or expressing it clearly, \( P(A \text{ and } B) \) must equal approximately 33%.
Thus, the answer is: A. 33%