Rule of probability applied to Genetics problems

Independence 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. Rearranging this last equation as P(AB)/P(A)=P(B), we see that if P(A|B)=P(A), then also P(B|A)=P(B). Examples: If P(A)=.5, P(B)=.4, and P(AB)=.2, then P(A|B)=.2/.4=.5 = P(A) and A and B are independent. If P(A)=.6, P(B)=.4, and P(AB)=.2, then P(A|B)=.2/.4=.5 which is not equal to .6=P(A), and A and B are not independent. Product rule for independent events If A and B are independent, P(AB)=P(A)P(B) (because P(A|B)=P(A) for independent events). (Example: If A and B are independent and P(A)=.3 and P(B)=.6, then P(AB)=.3 × .6 = .18.) N.B.: If A and B are disjoint (which includes the case where A and B are complementary) P(AB)=0 P(A|B)=0=P(B|A) #Genetics #DNA #ruleOfProbability #productRule #statictics