Stat 333 - Tutorial 1 1. Two events A and B are mutually exclusive with P ( A ) = 0 . 25 and P ( B ) = 0 . 3 . Find: i) P ( A ∪ B ) ii) P ( ¯ A ∪ ¯ B ) 2. You are given that the sample space S = A ∪ B where P ( A ) = 0 . 55 and P ( 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 heads 75 percent of the time. When one of the three coins is selected at random and ﬂipped, it shows 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 in statistics. Springer-Verlag, 1985. Section 3.6 Problem #14.) A gambler is told that one of two slot machines pays off with probability p 1 , while the other pays off with probability p 2 < p 1 . Once a machine has been selected, successive plays are independent. The
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