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prelim2answerkey - Introduction to Statistics Prelim#2 PAM...

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Introduction to Statistics- Prelim #2 PAM 2100 Spring 2009 STUDENT’S NAME: Answer Key SECTION NUMBER:_____________________________________________ CIRCLE YOUR ANSWERS TO THE MULTIPLE CHOICE QUESTIONS. ANSWER THE PROBLEMS IN THIS EXAMINATION. WHEN YOU START, MAKE SURE YOUR EXAM HAS 8 PROBLEMS AND 15 MULTIPLE CHOICE QUESTIONS. THE EXAM HAS 13 PAGES INCLUDING THIS COVER PAGE. THE EXAM IS OUT OF 100 POINTS. THE 8 PROBLEMS ARE WORTH 70 POINTS AND THE 15 MULTIPLE CHOICE QUESTIONS ARE WORTH 30 POINTS. ALLOCATE YOUR TIME ACCORDINGLY. YOU HAVE 2 HOURS TO COMPLETE THIS EXAM. DO NOT WRITE ANY NOTES OR FORMULAS ON THE FRONT OR BACK OF THE EXAM OR ON TABLE A. MAKE SURE YOU CHECK ALL YOUR FINAL ANSWERS.

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PROB 1_____ PROB 2______ PROB 3______ PROB 4______ PROB 5______ PROB 6_____ PROB 7______ PROB 8_______ MC________ TOTAL_________ (Correct final answers receive full credit. Showing work is not necessary for full credit) Problem 1 (8 points) Dugout Lou thinks that the probabilities for the American League Baseball champion are as follows: The Yankees have probability 0.1 of winning. The Red Sox and Angels have equal probability of winning. The winning probability of the Athletics is one- fourth that of the Red Sox or Angels. No other team has a chance. What is Lou’s assignment of probabilities to teams? Round your final answers to four decimal places if necessary. Ans: Let the probability of winning for Red Sox or Angels be x. Then the Athletics’ probability of winning is (1/4)x. Since all probabilities must sum up to 1, x+x+(1/4)x+0.1=1 or, (9/4)x=9/10 so, x=.4 So, P(Red Sox winning)=P(Angels winning)=.4, P(Athletics winning)=P(Yankees winning)=.1 ( 2 points for each of the correct probabilities) 2 2
Problem 2 (10 points) Each of us has an ABO blood type, which describes whether two characteristics called A and B are present. Every human being has two blood type alleles (gene forms), one inherited from our mother and one from our father. Each of these alleles can be A, B, or O. Which two we inherit determines our blood type. Here is a table that shows what our blood type is for each combination of two alleles: Alleles inherited Blood type A and A A A and B AB A and O A B and B B B and O B O and O O We inherit each of a parent’s two alleles with probability 0.5. We inherit independently from our mother and father. Elise has alleles B and O. John has alleles A and O. They have three children. a) What is the probability that all three children have blood type A? Round your final answer to four decimal places if necessary. Elise and John’s children can have blood type A, B, AB, or O. For any child, 3 3

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P(type A) =0.5*O.5=.25 P(type B) = 0.5*0.5 = 0.25 P(type AB) = = 0.5*0.5 = 0.25 P(type O)=0.5*0.5=0.25 Now note that each child inherits alleles from the parents independently from the other children. Therefore, P(All three are type A)= P(first child is type A) * P(second child is type A) * P(third child is type A)=.25*.25*.25 =.0156 (5 points) b) What is the probability that all three children have the same blood type? Round your final answer to four decimal places if necessary.
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prelim2answerkey - Introduction to Statistics Prelim#2 PAM...

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