Suppose C1 and C2 form a partition of sample space S. Suppose A and B are two events such that the following statements are true. Are A and B independent? a. A and B are conditionally independent given C1 b. A and B are conditionally independent given C2 c. B and C1 are independent d. B and C2 are independent

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Isiah

6 December, 03:11

Suppose C1 and C2 form a partition of sample space S. Suppose A and B are two events such that the following statements are true. Are A and B independent? a. A and B are conditionally independent given C1 b. A and B are conditionally independent given C2 c. B and C1 are independent d. B and C2 are independent

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Dwayne · Answer 1

Option b. A and B are conditionally independent given C2.

Explanation:

The conditional probability of an event is the probability that a given event will occur given that another event, say A has already occurred.

In a case where events A and B are independent (in this case, where the probability of A has no effect on the probability of B occurring), the conditional probability of an event B given that A has taken place is simply the probability of the event A.

If the two events are not independent, then the probability of an event occurs as an intersection of set A and B.