Thus we can say, in notation, that A and B are independent events if: P(B A) = P(B) In words this says, given A happens, the probability of B has not changed - it is the same as P(B) overall
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If so, A and B are independent events, otherwise they are not Example: Suppose data showed that smokers and non- smokers are equally likely to get the flu P(flu
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If B = A or B = A , A and B are not independent except in the above trivial case when P(A) or P(B) is 0 or 1 In other words, an event A which has probability strictly
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If A and B are independent events with P(A)=0 6 and P(B)=0 3, find the following: (a) P(A U B) (b) P(A n B) (c) P(A U B ) (d) P(AB) (e) P(B A ) (a) P(A U B) = P(A)
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P(A ∩ B ∩ C) = P(A)P(B)P(C) Definition We say that the events A1,A2, ,An are mutually independent if for all 1 ≤ i1 < i2
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none of these Correct Answer 3 Explanation A B = ∩ φ ∩ φ ∩ φ ∩ φ Q No 3 If A and B are independent events, then which of the following is not true
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(20 pts ) Conditional Independence and Medical Diagnosis In class we have defined the notion of independence of events: two events A and B are independent if
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B ⊆ Ω The conditional probability of event B, given event A, is P(B A) = Definition: Events A and B are statistically independent if and only if P(A ∩ B)
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The conditional probability of an event B, given event A is denoted P(B A) Two events are independent if the occurrence of one does not affect the probability
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