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MAT 142 Summer Session 1 ANSWERS Homework Day #11: Name:______________________ I. The nature of Probability and II. Theoretical Probability Navigate to http://www.regentsprep.org/Regents/Math/probab/theoProp.htm and quickly read the contents to review the difference between empirical probability and theoretical probability. 1. The probability of an event occurring will always be a number between what other two numbers? 0 P( E ) 1 The color of the last 30 cars to enter GCC’s parking lot were 14 Blue, 10 Red and 6 White. Use this information to determine the empirical probability that the next car to enter GCC’s parking lot is… 2. Blue 7 15 3. Red 4. White 1 3 1 5 In a particular week a vet treated the following animals. Animal Dog Cat Bird Rabbit Number Treated 45 40 15 5 Determine the empirical probability that the next animal the vet treats is… 5. A Dog 3 7 6. Cat 8 21 7. Rabbit 1 21 Navigate to http://www.regentsprep.org/Regents/Math/probab/PracEmp.htm and try the six problems on that web page. Be sure to try the problems yourself BEFORE reading the explanation that tells you the answer! 8. How did you do on those six problems? I got 6 out of 6 !!!! (How would you do if I put these on a test or quiz? A multiple choice test has five possible answers for each question. 9. If you guess at an answer for a particular question what is the probability that you get the correct answer? (write your answer as a fraction AND a decimal AND a percent). 1 .2 20% 5 10. If you eliminate one of the five answers and guess from the remaining possibilities what is the probability that you get the correct answer? (write your answer as a fraction AND a decimal AND a percent). 1 .25 25% 4 Navigate to http://www.regentsprep.org/Regents/Math/probab/PracThoe.htm and try the five problems on that web page. Be sure to try the problems yourself BEFORE looking at the answer! 11. How did you do on those five problems? I got 5 out of 5 !!!! (How would you do if I put these on a test or quiz? One card is selected at random form a standard deck of playing cards. Determine the probability that the card selected is… 12. a 3 13. a 4 or a 10 1 13 14. the seven of hearts 1 4 1 2 1 52 2 13 16. a diamond 15. a red card 17. a black or a red card 18. a heart and a club 1 0 19. Which of the following is an experiment? (circle the correct answer) A. Tossing a Coin B. Rolling a single six sided die C. Choosing a Marble from a Jar D. All of these. 20. A glass jar contains 6 red, 5 green, 8 blue and 3 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of choosing a red marble? a green marble? a blue marble? a yellow marble? P(Red) = 3 11 P(Green) = 5 22 P(Blue) = 4 11 P(Yellow) = 3 22 21. Which of the following is an outcome? (circle the correct answer) ] A. Rolling a Pair of Dice B. Landing on Red C. Choosing 2 marbles from a jar E. None of these. 22. Which of the following experiments do NOT have equally likely outcomes? (circle the correct answer) A. Choosing a number a natural number at random from 1 to 7. B. Toss a coin C. Choosing a letter at random from the word SCHOOL D. None of these 23. What is the probability of choosing a vowel from the English alphabet? 5 26 24. A natural number from 1 to 11 is chosen at random. What is the probability that it is odd? 6 11 Navigate to http://www.cc.gatech.edu/classes/cs6751_97_winter/Topics/stat-meas/probHist.html and read the article “A Short History of Probability” 25. According to this article…. “Mathematical statistics is one important branch of applied probability; other applications occur in such widely different fields as genetics, psychology, economics, and engineering.”