Two events, A and B, are independent if:
Click on the arrows to vote for the correct answer
A. B. C. D.D
This is the definition of independence.
The correct answer is D. P(A and B) = P(A) * P(B).
When two events, A and B, are independent, it means that the occurrence or non-occurrence of one event does not affect the probability of the other event happening. In other words, the probability of both events A and B occurring together is equal to the product of their individual probabilities.
Mathematically, if events A and B are independent, then the probability of both events occurring simultaneously (A and B) is given by:
P(A and B) = P(A) * P(B)
Here's a more detailed explanation:
Let's assume that P(A) represents the probability of event A happening, and P(B) represents the probability of event B happening. If events A and B are independent, the probability of both events occurring together (P(A and B)) can be calculated as follows:
Since A and B are independent, the occurrence of event A does not impact the occurrence of event B, and vice versa. Therefore, the probability of both events happening simultaneously is the product of their individual probabilities.
For example, if the probability of event A happening is 0.3 (or 30%) and the probability of event B happening is 0.4 (or 40%), the probability of both events happening simultaneously (A and B) would be:
P(A and B) = P(A) * P(B) = 0.3 * 0.4 = 0.12 or 12%
This means that there is a 12% chance of events A and B occurring together if they are independent.
In summary, if two events A and B are independent, the probability of both events occurring together (P(A and B)) is equal to the product of their individual probabilities (P(A) * P(B)). Therefore, option D. P(A and B) = P(A) * P(B) is the correct answer.