Problems 199 10. Compare the Poisson approximation with the correct binomial probability for the following cases: (a) P{X = 2} when n = P(X =0} whenn= 10, p .13; (c) P{X = 4} when n = 9, p= .2. 10,p .13; %3D %3D %3D 11. If you buy a lottery ticket in 50 lotteries, in each of which your chance of winning a prize is T00 what is the (approximate) probability that you will win a prize (a) 100 at least once, (b) exactly once, and (c) at least twice? 12. The number of times that an individual contracts a cold in a given year is a Poisson random variable with parameter 2 = 3. Suppose a new wonder drug (based on large quantities of vitamin C) has just been marketed that reduces the Poisson parameter to 2 = 2 for 75 percent of the population. For the other 25 percent of the population, the drug has no appreciable effect on colds. If an individual tries the drug for a year and has 0 colds in that time, how likely is it that the drug is beneficial for him or her? %3D 13. In the 1980s, an average of 121.95 workers died on the job each week. Give estimates of the following quantities: (a) the proportion of weeks having 130 deaths or more; (b) the proportion of weeks having 100 deaths or less. Explain your reasoning. 14. Approximately 80,000 marriages took place in the state of New York last Estimate the probability that for at least one of these couples year. (a) both partners were born on April 30; (b) both celebrated their birthday on the same day of the year. partners State your assumptions. 15. The game of frustration solitaire is played by turning the cards of a randomly shuffled deck of 52 playing cards over one at a time. Before you turn over the you turn first card, say ace; before you turn over the second card, say two, over the third card, say three. Continue in this manner (saying ace again before turning over the fourteenth card, and so on). You lose if you ever turn over a card that matches what you have just said. Use the Poisson paradigm to approximate the probability of winning. (The actual probability is .01623.) before 16. The probability of error in the transmission of a binary digit over a communica- tion channel is 1/103. Write an expression for the exact probability of more than 3 errors when transmitting a block of 103 bits. What is its approximate value? Assume independence.

Problems 199 10. Compare the Poisson approximation with the correct binomial probability for the following cases: (a) P{X = 2} when n = P(X =0} whenn= 10, p .13; (c) P{X = 4} when n = 9, p= .2. 10,p .13; %3D %3D %3D 11. If you buy a lottery ticket in 50 lotteries, in each of which your chance of winning a prize is T00 what is the (approximate) probability that you will win a prize (a) 100 at least once, (b) exactly once, and (c) at least twice? 12. The number of times that an individual contracts a cold in a given year is a Poisson random variable with parameter 2 = 3. Suppose a new wonder drug (based on large quantities of vitamin C) has just been marketed that reduces the Poisson parameter to 2 = 2 for 75 percent of the population. For the other 25 percent of the population, the drug has no appreciable effect on colds. If an individual tries the drug for a year and has 0 colds in that time, how likely is it that the drug is beneficial for him or her? %3D 13. In the 1980s, an average of 121.95 workers died on the job each week. Give estimates of the following quantities: (a) the proportion of weeks having 130 deaths or more; (b) the proportion of weeks having 100 deaths or less. Explain your reasoning. 14. Approximately 80,000 marriages took place in the state of New York last Estimate the probability that for at least one of these couples year. (a) both partners were born on April 30; (b) both celebrated their birthday on the same day of the year. partners State your assumptions. 15. The game of frustration solitaire is played by turning the cards of a randomly shuffled deck of 52 playing cards over one at a time. Before you turn over the you turn first card, say ace; before you turn over the second card, say two, over the third card, say three. Continue in this manner (saying ace again before turning over the fourteenth card, and so on). You lose if you ever turn over a card that matches what you have just said. Use the Poisson paradigm to approximate the probability of winning. (The actual probability is .01623.) before 16. The probability of error in the transmission of a binary digit over a communica- tion channel is 1/103. Write an expression for the exact probability of more than 3 errors when transmitting a block of 103 bits. What is its approximate value? Assume independence.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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