STATS 2B03 Lecture : some basic probability concepts (2).docx
19 Jun 2013
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Example: p(person is left-handed or that their parents are both right handed) P(l or rr) = p(l) + (rr) p(l and rr) = Rule p5: if a and b are independent then p(a b)=p(a) x p(b) Example: suppose that each child has probability of inheriting a certain disease. If a family of 2 children the probability that both children inherit the disease is: p(d and d) = p(dd) = p(d) x p(d) = . How do you know when to add or multiply: or add, and multiply. Example: in a family of 4 children (a) p(none inherit the disease)=p(nnnn) P(n) p(n) p(n) p(n)= (b) p(exactly 1 inherits the disease)=p(dnnn or ndnn or nndn or nnnd) P(dnnn)+p(ndnn)+p(nndn)+p(nnnd)=( ) 4 (c) p(at least 1 inherits the disease)=1-p(nnnn) Conditional probability of b given a: p(b(a)), is the probability that the event b occurs, given that the event a has already occurred.
