Three couples are invited to a dinner party

 1. Three couples are invited to a dinner party. They will independently show up with probabilities 0.9, 0.8, and 0.75 respectively. Let N be the number of couples that show up. Calculate the probability that N = 2 2. Statistics show that 5% of men are color blind and 0.25% of women are color blind. If a person is randomly selected from a room with 35 men and 65 women, what is the likelihood that they are color blind? 3. Do Exercise 26 on page 14 of the book. 4. On a multiple choice exam with four choices for each question, a student either knows the answer to a question or marks it at random. Suppose the student knows the answers to 60% of the exam questions. If he marks the answer to question 1 correctly, what is the probability that he knows the answer to that question? 5. In a certain city, 30% of the people are conservative, 50% are liberals, and 20% are independents. In a given election, 2/3 of the conservatives voted, 80% of the liberals voted, and 50% of the independents voted. If we pick a voter at random, what is the probability that this person is a liberal? 6. Let (;F; P) be a probability space and suppose that fAng1 n=1 is an increasing sequence of events. For each integer n 1, set Cn = A1 if n = 1 An n An??1 for n 2: Show that the Cn's are mutually disjoint and that 1[n=1An = 1[n=1Cn : 1 2 SPRING 2013 7. Let (;F; P) be a probability space and suppose that fAng1 n=1 is a sequence of events. Set Bn = 1[ m=nAm and Cn = 1\ m=nAm It is clear that Bn is a decreasing sequence of events, while Cn is an increasing sequence of events. Show that B = 1\n=1Bn = f! 2 : ! 2 An for innitely many values of ng andC = 1[n=1Cn = f! 2 : ! 2 An for all but nitely many values of ng 8. Do exercise 4 on page 24 of the book. 9. Suppose we roll two fair 6-sided dice. Let X be a random variable corresponding to the minimum value of the two rolls

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