If P(A)=48% and P(B)=87% , what must P(A and B) equal to prove that P(A) and P(B) are independent events? (1 point) Responses 42% 42% 35% 35% 48% 48% 68% 68%

Answer 1

For two events A and B to be independent, the probability of both events occurring together, \( P(A \text{ and } B) \), must equal the product of the probabilities of each event occurring individually. This can be expressed as:

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

Given that \( P(A) = 48% = 0.48 \) and \( P(B) = 87% = 0.87 \), we can calculate:

\[ P(A \text{ and } B) = 0.48 \times 0.87 \approx 0.4176 \]

Converting this to a percentage gives:

\[ P(A \text{ and } B) \approx 41.76% \]

Rounded to the nearest percentage, this is approximately 42%.

Therefore, to show that A and B are independent events, \( P(A \text{ and } B) \) must equal 42%.