Chapter 3. Probability

Chapter 3: Probability 7312. Clinical Trials of Pregnancy Test11P(negative test and not pregnant) 99 0.1111= = =P(negative test) 16 0.161699P(not pregnant | negative test)= 0. 688There is a 0.688 probability that she will not be pregnant when the test is negative. This is not the same as theprobability of getting a negative test when she is not pregnant, which is 0.786 as found in problem 11.13. Redundancy in Alarm Clocks, failure rate per clock is 0.01P(at least one would work)= 1 – P(none of the three would work)P(none of the three would work)= P(first will fail) ∗ P(second will fail) ∗ P(third will fail) =(0.01 ∗ 0.01∗ 0.01)= 0.000001P(at least one would work)= 1 – 0.000001= 0.999999The surgeon certainly does gain by using three alarm clocks compared with one. If she used one, we wouldexpect a failure one day out of every 100 days, but if she used three, we would expect a failure one out of every1,000,000 days.14. Acceptance Sampling, 3% defectiveP(at least one defect)= 1 – P(none of the ten samples are defective)=1 – [P(first is not defective) ∗ P(second is not defective) ∗…∗ P(tenth is not defective)]=1 – 0.97 10 = 1 – 0.737= 0.26315. Using Composite Blood Sampling, 0.1 are positive for HIVP(at least one positive)= 1 – P(none are positive)=1 – [P(first is not positive) ∗ P(second is not positive) ∗ P(third is not positive)=1 – (0.9 ∗ 0.9 ∗ 0.9)= 1 – 0.729= 0.27116. Using Composite Water Samples, 2% chance of E. coli bacteriaP(at least one positive sample)= 1 – P(none of the six samples are positive)=1 – [P(first is not positive) ∗ P(second is not positive) ∗…∗ P(sixth is not positive)]=1 – 0.98 6 = 1 – 0.886= 0.114Conditional Probabilities. In Exercises 17-20, use the Titanic mortality data in the accompanying table.Men Women Boys Girls TotalSurvived 322 318 29 27 696Died 1360 104 35 18 1517Total 1682 422 64 45 2213number of men who died 1360number who died 1517number of men who died 1360P ( died | men) == = 0.number of men 168217. P ( man | died) == = 0. 89718. 809number of boys and girls who survived 5619. P ( boy or girl | survived) == = 0. 0805number who survived 696number of men and women who died 1464P ( man or woman | died) == =number who died151720. 0. 965