Stat 333 - Tutorial 11. Two eventsAandBare mutually exclusive withP(A) = 0.25andP(B) = 0.3. Find:i)P(A∪B)ii)P(¯A∪¯B)2. You are given that the sample spaceS=A∪BwhereP(A) = 0.55andP(B) = 0.6. Find:i)P(A∩B)ii)P(B|A)iii)P(B|¯A)3. (Chapter 1 Problem #42 of the textbook.) There are three coins in a box. One is a two-headed coin, another is a fair coin, and the third is a biased coin that comes up heads75 percent of the time. When one of the three coins is selected at random and flipped, itshows heads. What is the probability that it was the two-headed coin?4. (J.G. Kalbfleisch. Probability and statistical inference. Number v. 1 in Springer texts instatistics. Springer-Verlag, 1985. Section 3.6 Problem #14.) A gambler is told that one oftwo slot machines pays off with probabilityp1, while the other pays off with probabilityp2< p1.Once a machine has been selected, successive plays are independent.Thegambler selects one machine at random and plays that machinentimes.
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