Question

If P(A)=51 % and P(B)=65 %, what must P(A and B) equal to prove that P(A) and P(B) are independent events?

A. 33%
B. 51%
C. 65%
D. 58%

Answer 1

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%**