# Probability and Random Selection

1) When writing about the probability that it will rain in Boston on July 4 of next year, a newspaper reporter states that the probability is 1/2, because either it will rain or it will not. Is this reasoning correct?

2) In a recent year, 389 of the 281,421,906 people in the United States were struck by lighting. Estimate the probability that a randomly selected person in the United States will be struck by lightning this year?

3) The US General Accounting Office tested the IRS for correctness of answers to taxpayers questions. For 1733 trials, the IRS was correct 1107 times and wrong 626 times.

a. Estimate the probability that a randomly selected taxpayers questions will be answered incorrectly.

b. Is it unusual for the IRS to provide a wrong answer to a taxpayers question? Should it be unusual?

4) The probability of the horse Outta Here winning the 129th Kentucky Derby was 1/50. What were the actual odds against Outta Here winning that race?

5) When the horse Funny Cide won the 129th Kentucky Derby, a $2 bet that Funny Cide would win resulted in a return of $27.60.

a. How much net profit was made from a $2 win bet on Funny Cide?

b. What were the payoff odds against a Funny Cide win?

c. Based on preliminary wagering before the race, bettors collectively believed that Funny Cide had a 2/33 probability of winning. Assuming that 2/33 was the true probability of a Funny Cide victory, what were the actual odds against his winnings?

d. If the payoff odds were the actual odds found in Part (c), how much would a $2 ticket be worth after the Funny Cide win?

6) If an event is the complement of another event, must those two events be disjoint?

7) Finding Complements

a. Find P(A) given that P(A) = 0.01.

b. A Reuters/zogby poll showed that 61% of Americans say they believe that life exists in the galaxy. What is the probability of randomly selecting someone not having that belief?

8) Use the table to answer the following:

Pedestrian intoxicated?

Yes No

Yes 59 79

Driver intoxicated No 266 581

a) If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was not intoxicated.

b) If one of the pedestrian deaths is randomly selected, find the probability that the driver was intoxicated or the pedestrian was not intoxicated.

9) The professor in a class of 25 students randomly selects a student, then randomly selects a second student. If all students are available for the second selection, is this sampling with replacement or sampling without replacement? Is the second outcome independent of the first?

10) A new computer owner creates a password consisting of two characters. She randomly selects a letter of the alphabet for the first character and a digit (0,1,2,3,4,5,6,7,8,9) for the second character. What is the probability that her password is K9? Would this password be effective as a deterrent against someone trying to gain access to her computer?

11) In a Riverhead, New York, case, nine different crime victims listened to voice recordings of five different men. All nine victims identified the same voice as that of the criminal. If the voice identifications were made by random guesses, find the probability that all nine victims would select the same person. Does this constitute reasonable doubt?

12) Use the following table to assist in problem:

Pedestrian intoxicated?

Yes No

Yes 59 79

Driver intoxicated No 266 581

a) If one of the pedestrian deaths is randomly selected, what is the probability that it involves an intoxicated pedestrian and an intoxicated driver?

b) If two different pedestrian deaths are randomly selected, what is the probability that in both cases, both the pedestrian and the driver were intoxicated?

c) If two pedestrian deaths are randomly selected with replacement, what is the probability that in both cases, both the pedestrian and the driver were intoxicated?

d) Compare the results from parts (b) and (c).

13) 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?

14) Republican Democrat Indepent

Male 46 39 1

Female 5 9 0

a) If we randomly select one Senator, what is the probability of getting a male, given that a Republican was selected?

b) If we randomly select one Senator, what is the probability of getting a Democrat or Independent, given that a male was selected?

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Solution contains answers of 14 problems.