Independent events

How do you show that two events are independent? Thanks!

With probabilities, you can see if two events are independent in two different ways. (1) P(A and B) = P(A) x P(B) or P(A given B)= P(A)

If P(B) = P (B|A) then A and B are independent.

For example:

P(having a female child) = 0.5

P(having a female child|the first child was female) = 0.5

The sex of the first child does not affect the probability. The probabilities are the same and therefore the events are independent.

that is a unit 4 (probability) topic! but to show two events are independent you can verify that the AND Probability of both events {P(A and B)} = the probability of both events multiplied {P(A)*P(B)}

The best and easiest way to show that two events are independent is usually done with a 2-way table. If you want to show that events A and B are independent, then find the probability of each, and multiply these probabilities together to see if it equals the probability of A AND B occuring. If so, the events are independent.

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