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p(a) = 1/3, p(b) = 1/2, p(a and b) = p(a)*p(b) = 1/6
If A and B are mutually exclusive, P(A or B)=P(A) + P(B) They both cannot occur together. For example: A die is rolled. A = an odd number; B= number is divisible by 2. P(A or B) = 1/3 + 1/3 = 2/3
Sum Rule: P(A) = \sum_{B} P(A,B) Product Rule: P(A , B) = P(A) P(B|A) or P(A, B)=P(B) P(A|B) [P(A|B) means probability of A given that B has occurred] P(A, B) = P(A) P(B) , if A and B are independent events.
P(A|B)= P(A n B) / P(B) P(A n B) = probability of both A and B happening to check for independence you see if P(A|B) = P(B)
If they're disjoint events: P(A and B) = P(A) + P(B) Generally: P(A and B) = P(A) + P(B) - P(A|B)