Math 425 All Answers Correct

Math 425 All Answers Correct (x+y)^n= the sum from k=0 to k=n of: [(n choose k)*x^(n-k)*y^k (x1+x2+...+xr)^n= the sum over all n1,n2...,nr such that n1+n2+...+nr=n of: [(n choose n1,n2,...,nr)*x1^n1*x2^n2+...+xr^nr Probability space ... How many ways to pair up 20 people 20!/(2^10*10!) How many handshakes in 20 person room? 20 choose 2 Sample Space The set of all possible outcomes of an experiment Event Any subset of the sample space Mutually Exclusive Two events, A and B, such that A intersect B is the empty set The Two Versions of the Distributive Laws 1. A intersect (B union C)=(A intersect B) union (A intersect C) 2. A union (B intersect C) = (A union B) Intersect (A union C) Demorgan's Law 1. (A union B)^c=A^c intersect B^c 2. (A intersect B)^c=A^c union B^c State the three probability axioms A probability function is a junction with a domain of all events within sample space, S, with the properties: 1. 0=P(A) for all A in S 2. P(S)=1 3. For any sequence of mutually exclusive events, E1,E2..., P(E1 union E2 union E3...)=P(E1)+P(E2)+P(E3)+... State 1. P(the empty set)=0 2. P(A^c)=1-P(A) 3. If A is a subset of B, P(A)=P(B) 4. P(A union B)=P(A)+P(B)-P(A intersection B) 5. P(A intersection B^c)=P(A)-P(A intersect B) 6. P(A)=1 State the exclusion inclusion principle for multiple events P(A1 union A2 union A3...)=P(A1)+P(A2)+P(A3)+...-P(A1 intersect A2)-P(A1 intersect A3)-P(A2 intersect A3)-...+P(A1 intersect A2 intersect A3)+P(A1 intersect A2 intersect A4)-... If E and F are mutually exclusive events of an experiment and independent trials are performed the event E will occur before the event F with probability: P(E)/(P(E