URGENT help needed with statistics, probability 1. The problem statement, all variables and given/known data 1) A plane functions iff at least 2 of its 3 engines function. P(each engine functions)=p, the engines operate independently of each other. Find the probability that the plane functions. 3. The attempt at a solution A=engine 1, B=engine 2, C=engine 3. P(plane functions)= P(AuB)+P(AuC)+P(BuC) P(AnBnC)=p3 P(AnB)=P(AnC)=P(BnC)=p2 P(AuBuC)=P(A)+P(B)+P(C)-P(AnB)-P(AnC)-P(BnC)-P(AnBnC)=3p-3p2-p3 http://img168.imageshack.us/img168/2991/venn.jpg [Broken] But the regions they want are P(AuB)+P(AuC)+P(BuC) which is just 3(p-p2-2p3) 1. The problem statement, all variables and given/known data 2) 2% of products in a factory are defective. Products are sold in packages of 100. What proportion of cartons contain at least 'x' defective products? x=1,2,3,...,100. (use binomial distribution) 2. Relevant equations Binomial distribution: P(X=x) = nCx px(1-p)n-x , where p is the probability of success. 3. The attempt at a solution P(defective)=0.02 P(not defective)=0.98 I need to get X~Bin(100,0.98) P(X=x)= 100Cx0.98x0.02100-x So my answer is just P(X=x)/100 ? (replacing P(X=x) with the above) 1. The problem statement, all variables and given/known data 3) A shipment of 8 items contain 3 that are defective. A person makes a random selection of 2 of these items, find the probability distribution for the number of defectives X. Find the cumulative functions of X as well. 3. The attempt at a solution So P(X=x) is defined as follows: 0 for x<1 3/8 for 1<x<2 5/56 for 2<x<3 ( 2 defective is 3/8 * 2/7) 6/336 for x>3 (3 defective is 3/8 * 2/7 *1/6) And to get the cdf I just integrate the functions (in the regions) between 'x' and -infinity?