What must be true in order for P(A OR B)=P(A) +P(B)?
a and b cannot be disjoint
a and b must be independent
a and b cannot be independent
a and b must be disjoint
it is always true
2. What must be true for P(A and B)=p(A) * P(B)
a and b cannot be independent
a and b must be disjoint
a and b cannot be independent
1. must be disjoint
2. For P(A and B) = P(A) * P(B) to be true, a and b must be independent.
The correct answer for the first question is: "a and b must be disjoint." In order for the probability of either event A or event B to be equal to the sum of their individual probabilities, it means that the events A and B cannot overlap or occur simultaneously. If events A and B were not disjoint, their probabilities would overlap, and simply adding their individual probabilities would result in counting the overlapping parts twice. Thus, the events A and B must be disjoint for P(A OR B) = P(A) + P(B) to hold.
The correct answer for the second question is: "a and b must be independent." For the probability of both event A and event B to be equal to the product of their individual probabilities, it means that the occurrence of one event does not affect the occurrence of the other. In other words, the events A and B must be independent. If events A and B were not independent, their probabilities would be affected by each other, and multiplying their individual probabilities would not accurately represent the probability of both events occurring together. Thus, events A and B must be independent for P(A and B) = P(A) * P(B) to hold.
1. A and B must be disjoint
2. A and B must be independent
2/2 correct 100%