Answer Happy

Problem #1: (10pts) If P(A) = 0.3 and P(B) = 0.2 and P( AB) = 0.1. Determine the following probabilities: a) PCA) b) P(AUB) c) P(A' n B) d) P(AN B') e) P(AU B') AP(AUB) are that: Problem #2: (10pts) a) If the sets х and Y non-mutually exclusive, show P(XUY)= P(X) + P(Y) - P( XY). b) Given two events х and Y draw Venn diagram demonstrate P(X) = P( XY)+P( XY), and deduce that P(X)=P(XVY)P(Y) + P(X7PODO a to that Problem #3: (15pts) Consider two events X and Y with probabilities, PX) = 7/15, P( XY)=1/3. and PCX,Y)= 2/3. Calculate P(Y). PYX), and P(Y/X). State with reasons whether the events X and Y are dependent or mutually exclusive Problem 2.93 from textbook (6th edition): (10pts) The following table summarizes the number of deceased beetles under autolysis (the destruction of a cell after its death by the action of its own enzymds) and putrefaction (decomposition of organic matter especially protein, by microorganisms, resulting in production of foul-smelling matter): Autolysis Putrefaction High Low High 14 30 Low 47 9 (a) If the autolysis of a sample is high, what is the probability that the putrefaction is low? (b) If the putrefaction of a sample is high, what is the probability that the autolysis is high? (c) If the putrefaction of a sample is low, what is the probability that the autolysis is low?