Respuesta :
The correct options are:
b) If A and B are independent , then P(A|B)=P(A)
c) If A and B are disjoint, then they cannot be independent
d) If A and B are disjoint, then P(A cap B)=0
Explanation:
a) If A and B are disjoint, then P(A) and P(B) must not equal each other because the sets have no elements in common. This means that the probability of any given event happening in either set is 0, and so P(A) and P(B) cannot be the same.
b) If A and B are independent, then P(A|B) = P(A) because the event that occurs in A has no impact on the probability of the event occurring in B. This is because the two events do not affect each other, so the probability of one happening does not change with the occurrence of the other.
c) If A and B are disjoint, then they cannot be independent because the two sets have no elements in common. This means that the events in A can affect the probability of events in B and vice versa. For example, if an event in A occurs, then it is impossible for an event in B to occur at the same time. This means that the events are not independent.
d) If A and B are disjoint, then P(A cap B) = 0 because the two sets have no elements in common.
e) They must not be independent because, Disjoint events are events that have no elements in common, so they cannot be independent since they are not related in any way. This means that the probability of A given B is also zero, which means that A and B cannot be independent.
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