What is P a B if A and B are independent?

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What is P a B if A and B are independent?

Two events A and B are called independent if P(A|B)=P(A), i.e., if conditioning on one does not effect the probability of the other. Since P(A|B)=P(AB)/P(B) by definition, P(A)=P(AB)/P(B) if A and B are independent, hence P(A)P(B)=P(AB); this is sometimes given as the definition of independence.

What is the formula for P A or B if A and B are not mutually exclusive?

If the events A and B are not mutually exclusive, the probability is: (A or B) = p(A) + p(B) – p(A and B).

For what value of P B would A and B be mutually exclusive?

= 0
If P(A AND B) = 0, then A and B are mutually exclusive.)

How do you find PA B?

We apply P(A ∩ B) formula to calculate the probability of two independent events A and B occurring together. It is given as, P(A∩B) = P(A) × P(B), where, P(A) is Probability of an event “A” and P(B) = Probability of an event “B”.

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Are the events A and B mutually exclusive?

It is the ANSWER to question (a). (b) Since P (A and B) is not equal to 0 (zero, ZERO), the events A and B are NOR mutually exclusive. ANSWER Notice : for mutually exclusive events X and Y, P (X and Y) = 0.

Are A and B mutually exclusive in conditional probability?

No, that’s only true when A and B are mutually exclusive. Let me try to make a distinction between them. The definition of conditional probability is given as follows; If the event A is independent of the event B, then that means that the probability that event A occurs is not affected by the probability of B.

What is p(b|a) in statistics?

For given two event A and B, P ( B | A) = P ( A | B) ∗ P ( B) / P ( A) = 0.1 ∗ 0.4 / 0.3 = 2 / 15 = 0.133 where P (B) is a prior distribution, P (A|B) is called likelihood, P (A) is called evidence (normalizing constant) and P (B|A) is posterior distribution. Let us understand what is happening in here by taking a very motivating example.

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What is the probability of the intersection of A and B?

Therefore, the probability of the intersection of A and B is nonzero. If both A and B were mutually exclusive, then the probability of the intersection would be 0. That’s not the case here. We can, therefore, conclude that independence does not imply mutual exclusivity. 8 clever moves when you have $1,000 in the bank.