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?(1 point) Responses 51% 51% 58% 58% 33% 33% 65%

Answer 1

To determine if events A and B are independent, we need to check if the probability of both events occurring together, P(A and B), satisfies the condition for independence:

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

Given:
- \( P(A) = 51\% = 0.51 \)
- \( P(B) = 65\% = 0.65 \)

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

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

Calculating this:

\[ 0.51 \times 0.65 = 0.3315 \]

Converting back to percentage form:

\[ 0.3315 = 33.15\% \]

Thus, for events A and B to be independent, \( P(A \text{ and } B) \) must equal 33.15%.

Therefore, among the responses given, the closest option corresponding to this is:

**33%**.