Question [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Two events are independent if ____
 A None of these are correct. B the two events occur at the same time C P(A | B) = P(A) or P(B | A) = P(B) D the probability of one or both events is greater than 1
Explanation:

Detailed explanation-1: -Let us now provide a formal definition of independence. Two events A and B are independent if and only if P(A∩B)=P(A)P(B). =P(A). Thus, if two events A and B are independent and P(B)≠0, then P(A|B)=P(A).

Detailed explanation-2: -In probability, we say two events are independent if knowing one event occurred doesn’t change the probability of the other event.

Detailed explanation-3: -If A and B are independent events, then the events A and B’ are also independent. Proof: The events A and B are independent, so, P(A ∩ B) = P(A) P(B). From the Venn diagram, we see that the events A ∩ B and A ∩ B’ are mutually exclusive and together they form the event A.

Detailed explanation-4: -Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B)

Detailed explanation-5: -To determine the probability of two independent events, A and B, both occurring, we multiply the probabilities of each of the two events together: P(A)×P(B)=P(A and B) . In some cases, the outcome of one event affects the outcome of a second event.

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