Independent if the occurrence or non occurrence of one event in no way affects

Independent if the occurrence or non occurrence of

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- Independent- if the occurrence, or non-occurrence of one event in no way affects the probability of another. - Conditional (dependent) – if the probability of one Event depends on another Event having taken place before. Addition Law- The Probability of 2 events P(A B) where is the union meaning the probability that either A or B occurs, or both. P(A B) = P(A or B) P(A or B) = P(A) + P(B) – P(A and B) P(A B) = the intersection of A and B.
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Mutually Exclusive Events If A and B are Mutually Exclusive Events, then P( A B) = 0. - They have no sample points in common, which means that when one occurs the other one cannot occur. - In this case the addition law becomes: P( A B) = P(A) + P(B) Conditional Probability P ( B | A ) = P ( A B ) P ( A ) = P ( A B ) P ( A ) P(B|A) = conditional probability (The Probability of B given A) The General Multiplication Rule This is used to estimate the intersection P( A B) of two events, or otherwise the probability of P(A and B). It is based on the definition of conditional probability. P ( B | A ) = P ( A B ) P ( A ) If the probability of A depends on the probability of B occurring first, then P(A and B) = P(A|B) x P(B) and P(A and B) = P(B|A) x P(A) If A and B are independent events, then the probability of A and B occurring is the product of the 2 probabilities. P (A and B) = P(A) x P(B) Checking for Independence P(A B) = P (A) x P(B) then events are independent P(A B) P(A) x P(B) then events are not independent Tree Diagram - A tree diagram is a graphical representation of probabilities - Each outcome is represented by a branch
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