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Practice Midterm 2 WI 10 Solutions

# Pg and m pgm pm 08 07 056 pg and f pgf pf 08 03 024 g

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P(G and M) = P(G|M) P(M) = (0.8) (0.7) = 0.56 P(G and F) = P(G|F) P(F) = (0.8) (0.3) = 0.24 G G C M 0.56 0.14 0.7 F 0.24 0.06 0.3 0.8 0.2 1 5

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Problems 24-26. Suppose the percentage of children in Tao’s karate class is 10% and the percentage of adults is 90%. Also suppose that 30% of the children are new to the class and 20 percent of the adults are new to the class. P(C) = 0.1 P(A) = 0.9 P(N|C) = 0.3 P(N|A) = 0.2 24. Using this information fill in a two-way table of all the probabilities (including all marginals). P(N and C) = P(N|C) P(C) = (0.3) (0.1) = 0.03 P(N and A) = P(N|A) P(A) = (0.2) (0.9) = 0.18 N N C C 0.03 0.07 0.1 A 0.18 0.72 0.9 0.21 0.79 1 25. What is the probability that someone in Tao’s karate class is new? (You can answer this with or without the table in #24.) P(N) = P(N and C) + P(N and A) = P(N|C) P(C) + P(N|A) P(A) = (0.3) (0.1) + (0.2) (0.9) = 0.03 + 0.18 = 0.21 ANS__ 0.21 ___ 26. What percentage of the new class members are children? (You can answer this with or without the table in #24.) 143 . 0 21 . 0 03 . 0 21 . 0 ) 1 . 0 )( 3 . 0 ( ) ( ) ( ) | ( ) ( ) ( ) | ( = = = = = N P C P C N P N P N and C P N C P ANS__ 0.143 ___ 6
Problems 27-30. The exam scores in Mr. Math’s class were: 40% A’s, 35% B’s, 25% C’s, No D’s and No E’s. Select two of his students at random and record their grades. P(A) = 0.4 P(B) = 0.35 P(C) = 0.25 27. Write down the sample space for this problem. S = {AA, AB, AC, BA, BB, BC, CA, CB, CC} 28. What is the chance that both people got the same grade? P(Both Same Grade) = P(AA or BB or CC) = P(AA) + P(BB) + P(CC) = P(A) P(A) + P(B) P(B) + P(C) P(C) = (0.4) (0.4) + (0.35) (0.35) + (0.25) (0.25) = 0.345 ANS__ 0.345 ____ 29. What is the chance that at least one of them got an A? Note that P(not A) = 1 – P(A) = 1 - .4 = .6 P(At least 1 A) = 1 – P(no A’s) = 1 – P(not A)^ 2 = 1 – (.6)^2 = 0.64 OR P(At least 1 A) = P(AA or AB or AC or BA or CA) = P(AA) + P(AB) + P(AC) + P(BA) + P(CA) = (0.4)(0.4) + (0.4)(0.35) + (0.4)(0.25) + (0.35)(0.4) + (0.25)(0.4) = 0.64 ANS____ 0.64 ____ 30. What is the chance that neither one got an A? P(Neither has an A) = 1 – P(At least 1 A) = 1 – 0.64 = 0.36 ANS__ 0.36 ________ 7

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ANSWER SHEET MC AND TF SOLUTIONS Stat 133 Midterm 2 WI 2010 THESE REPRESENT YOUR FINAL ANSWERS! BLANKS WILL RECEIVE 0 POINTS. 1. A B C D 2. A B C D 3. A B C D 4. A B C D 5. A B C D 6. A B C D 7. A B C D 8. A B C D 9. A B C D 10. A B C D 11. A B C D 12. A B C D 13. A B C D 14. A B C D 15. A B C D 16. A B C D 17. A B C D 18. A B C D 19. A B C D 20. A B C D 8
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PG and M PGM PM 08 07 056 PG and F PGF PF 08 03 024 G G C M...

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