Answer:
B. P(A and B) = 0.14
Explanation:
To determine if events A and B are independent, we need to check if the probability of their intersection, P(A and B), is equal to the product of their individual probabilities, P(A) and P(B).
If A and B are independent events, then P(A and B) = P(A) * P(B).
Given that P(A) = 0.70 and P(B) = 0.20, let's calculate their product:
P(A) * P(B) = 0.70 * 0.20 = 0.14
Now, let's evaluate the answer choices:
A. P(A or B) = 0.90:
This does not provide information about the intersection of A and B, so it doesn't help determine if A and B are independent.
B. P(A and B) = 0.14:
This matches the product of P(A) and P(B) calculated earlier. If this option is true, then A and B are independent events.
C. P(A or B) = 0.14:
This is the same value as the product of P(A) and P(B), but it represents the probability of their union (A or B). It doesn't provide information about their intersection, so it doesn't help determine if A and B are independent.
D. P(A and B) = 0:
This does not match the product of P(A) and P(B) calculated earlier. If this option is true, it would imply that A and B have no common outcomes, making them independent.
Therefore, based on the calculations, the correct option is:
B. P(A and B) = 0.14
If P(A and B) equals the product of P(A) and P(B), then events A and B are independent.