In: Statistics and Probability
PART 1 For each of the following statements, indicate symbolically the information given in the statement or the question. If you are not given a numeric value, then end your equation with a “?” Example: Given that the registered voter is an independent(I), the probability the voter opposes(O) the proposition is 0.80. Answer: P(O│I) = 0.80 1. The probability that a driver will be exceeding the speed limit (E) is 0.15. 2. When a new machine is functioning properly (F), only 3% of items produced are defective (D). 3. What is the probability that a randomly selected driver on the freeway will exceed the speed limit (E) and be stopped by the highway patrol (S)? 4. If a driver is exceeding the speed limit on the freeway (E), the probability that the driver will be stopped by the highway patrol (S) is 0.01. 5. If a driver is not exceeding the speed limit on the freeway (EC), the probability that the driver will be stopped by the highway patrol(S) is 0.001. 6. What is the probability that a driver on the freeway was neither stopped by the highway patrol (S) nor was exceeding the speed limit (E)? 7. What is the probability that a driver on the freeway who has been stopped by the highway patrol (S) was exceeding the speed limit (E)? 8. Past experience indicates that for 75% of successful bids (S) the agency requested additional information (I). 9. If a student goes to school full time (F), the probability that school quality is the first reason for choosing a school (Q) is 0.473. 10. What is the probability that a randomly chosen student goes to school full time (F) or has school quality as the first reason for choosing a school (Q)? 11. The Dallas IRS auditing staff believes that the probability of finding a fraudulent return (F) given that the return contains deductions for contributions exceeding the IRS standard (E) is 0.20.