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?(1 point)

Question

Responses

51%
51%

65%
65%

33%
33%

58%
58%

Answer 1

For two events A and B to be independent, the following condition must hold:

\[ P(A \text{ and } B) = P(A) \times P(B) \]

Given:

• \( P(A) = 51% = 0.51 \)
• \( P(B) = 65% = 0.65 \)

Now, we can calculate \( P(A) \times P(B) \):

\[ P(A) \times P(B) = 0.51 \times 0.65 = 0.3315 \]

So,

\[ P(A \text{ and } B) = 33.15% \]

The answer that matches this percentage (approximately) is 33%.

Thus, \( P(A \text{ and } B) \) must equal 33% to prove that A and B are independent events.