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MAT 155DY1 & DY2
Section 4.5 Complements & Conditional ProbabilitySection 4.6 Probabilities Through Simulations
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180/6. Describe the complement of the following: When 50 electrocardiograph units are shipped, all of them are free of defects.
Section 45 Multiplication Rule: Complements & Conditional Probability
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180/8. Describe the complement of the following: When Brutus asks 12 different women for a date, at least on of them accepts.
Section 45 Multiplication Rule: Complements & Conditional Probability
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180/10. Use subjective probability to estimate the probability of randomly selecting an adult and getting a male, given that the selected person owns a motorcycle. If a criminal investigator finds that a motorcycle is registered to Pat Ryan, is it reasonable to believe that Pat is a male?
Section 45 Multiplication Rule: Complements & Conditional Probability
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180/12. If a couple plans to have 10 children (it could happen), what is the probability that there will be at least one girl? If the couple eventually has 10 children and they are all boys, what can the couple conclude?
Section 45 Multiplication Rule: Complements & Conditional Probability
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Complements: The Probability of “At Least One”
P(at least one) = 1 – P(none)
The complement of getting at least one item of a particular type is that you get no items of that type.
[ P(x < 1 item) = P(x = 0 items)]
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Section 45 Multiplication Rule: Complements & Conditional Probability
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Definition
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Section 45 Multiplication Rule: Complements & Conditional Probability
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Intuitive Approach to Conditional Probability
The conditional probability of B given A can be found by assuming that event A has occurred and, working under that assumption, calculating the probability that event B will occur.
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Section 45 Multiplication Rule: Complements & Conditional Probability
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180/14. Refer to Table 41 (p. 169) and assume that 1 of the 300 test subjects is randomly selected. Find the probability of getting someone who tests positive, given that he or she did not use marijuana. Why is this particular case problematic for test subjects?
Section 45 Multiplication Rule: Complements & Conditional Probability
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180/16. Refer to Table 41 (p. 169) and assume that 1 of the 300 test subjects is randomly selected. Find the probability of getting someone who did not use marijuana, given that he or she tested negative. Compare these results with those in Exercise 15.
Section 45 Multiplication Rule: Complements & Conditional Probability
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Section 45 Multiplication Rule: Complements & Conditional Probability181/18. With one method of the procedure called acceptance sampling, a sample of items is randomly selected without replacement, and the entire batch is rejected if there is at least one defect. The Medtyme Company has just manufactured 5000 blood pressure monitors, and 4% are defective. If 3 of them are selected and tested, what is the probability that the entire batch will be rejected?
155S4.54.6.notebook
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February 08, 2010
Sep 157:22 AM
Section 45 Multiplication Rule: Complements & Conditional Probability181/18. With one method of the procedure called acceptance sampling, a sample of items is randomly selected without replacement, and the entire batch is rejected if there is at least one defect. The Medtyme Company has just manufactured 5000 blood pressure monitors, and 4% are defective. If 3 of them are selected and tested, what is the probability that the entire batch will be rejected?
Sep 157:22 AM
Section 45 Multiplication Rule: Complements & Conditional Probability
181/20. The Orange County Department of Public Health tests water for contamination due to the presence of E. coli (Escherichia coli) bacteria. To reduce lab costs, water samples from six public swimming areas are combined for one test, and further testing is done only if the combined sample fails. There is a 2% chance of finding E. coli bacteria in a public swimming area. Find the probability that a combined sample from six public swimming areas will reveal the presence of E. coli bacteria.
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Testing for IndependenceIn Section 44 we stated that events A and B are independent if the occurrence of one does not affect the probability of occurrence of the other. This suggests the following test for independence:
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181/22. If we randomly select one Senator, what is the probability of getting a male, given that a Republican was selected? Is this the same result found in Exercise 21?
Section 45 Multiplication Rule: Complements & Conditional Probability
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Definition: A simulation of a procedure is a process that behaves the same way as the procedure, so that similar results are produced.
Section 4.6 Probabilities Through Simulations
A TI83/84 Plus calculator can be used to simulate an experiment. Generate 25 integers from 1 to 365.
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185/6. When Mendel conducted his famous hybridization experiments, he used peas with green pods and yellow pods. One experiment involved crossing peas in such a way that 25% of the offspring peas were expected to have yellow pods, and 75% of the offspring peas were expected to have green pods. Describe a procedure for using a TI83/84 Plus calculator to simulate 12 peas in such a hybridization experiment.
Section 4.6 Probabilities Through Simulations
See Problem 10 for calculation of the mean number of times 1 occurred out of 12 randomly generated numbers 1 through 4 by the 21 persons in class.
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186/8. Fifteen percent of U.S. men are lefthanded. Describe a procedure for using a TI83/84 Plus calculator to simulate the random selection of 200 men. The outcomes should consist of an indication of whether each man is lefthanded or is not.
Section 4.6 Probabilities Through Simulations
Let 15 of the 100 numbers represent lefthanded men (15% of all men being lefthanded. To select 200 men, generate random integers 1 through 100 for 200 times.With the TI83/84 calculator, enter the following:randInt(1,100,200). Store these values in L1 and SortA(L1). Now count the number of numbers less than 16 as the number of lefthanded men of the 200 men.
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186/10. Use a TI83/84 Plus calculator to simulate the following (See Exercise 6).(a) Conduct the simulation and record the number of yellow pods. Is the percentage of yellow peas from the simulation reasonably close to the value of 25%?
Section 4.6 Probabilities Through Simulations
Twentytwo persons in class ran the simulation randInt(1,4,12) and recorded the number of 1’s represnting yellow pods. The average number of 1’s was 3.09 out of 12 runs or about 25% of the numbers were 1’s for yellow pods.
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186/10. (continued) Use a TI83/84 Plus calculator to simulate the following (See Exercise 6).(b) Repeat simulation for a total of 10 times recording the number of yellow pods. Based on the results, do the numbers of peas with yellow pods appear to be very consistent? Would it be unusual to randomly select 12 such offspring peas and find that none of them have yellow pods?
Section 4.6 Probabilities Through Simulations
The mean is 2.7 (27/10 = 2.7). This is about 22.5% of 12 such offspring peas have yellow pods.
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186/12. Use a TI83/84 Plus calculator to simulate the following (See Exercise 8).(a) Conduct the simulation and record the number of lefthanded men. Is the percentage of lefthanded men from the simulation reasonably close to the value of 15%?
Section 4.6 Probabilities Through Simulations
The mean of 31 lefthanded men is about 15.5% percent of the 200 men.
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186/12. (continued) Use a TI83/84 Plus calculator to simulate the following (See Exercise 8).(b) Repeat simulation for a total of 5 times recording the number of lefthanded men. Based on the results would it be unusual to randomly select 200 men and find that none of them are lefthanded?
Section 4.6 Probabilities Through Simulations