Question

In: Statistics and Probability

1) Many Americans use savings bonds to supplement retirement funds or to pay for qualified higher-education...

1) Many Americans use savings bonds to supplement retirement funds or to pay for qualified higher-education expenses. The U.S. Treasury even sells savings bonds online. Approximately one in every six Americans owns savings bonds. Suppose four Americans are randomly selected.

a) What is the probability that all own savings bonds?

b) What is the probability that none own savings bonds?

c) What is the probability that exactly two of the four own savings bonds (hint: need to think about how many arrangements there are)?

2) A friend who works in a big city owns two cars, one small and one large. Seventy-five percent of the time he drives the small car to work, and twenty-five percent of the time he drives the large car. If he takes the small car, he usually has little trouble parking, and is at work on time with probability 0.8. If he takes the large car, he is at work on time with probability 0.5. Drawing a tree diagram would be helpful.

a) What is the probability your friend arrives at work on time?

b) Given that he was on time on a particular morning, what is the probability that he drove the small car?

c) Are driving the small car and showing up to work on time independent or dependent events? Show mathematically how you know.

3) Suppose that in a survey of a large, random group of people, 17% are found to be smokers. Suppose further that 8% of the smokers and 1% of the non-smokers died of lung cancer. Drawing a tree time would be helpful.

a) What is the probability that a randomly selected person is a smoker and died of lung cancer?

b) What is the probability that a randomly selected person is a smoker or died of lung cancer?

c) What is the probability that a randomly selected person dies of lung cancer?

d) Given that a person died of lung cancer, what is the probability they were a smoker?

e) Are having lung cancer and being a smoker mutually exclusive? Show mathematically how you know.

f) Are having lung cancer and being a smoker independent? Show mathematically how you know.

Expert Solution

Let p be the probability that a randomly selected person

orchestra answered 1 year ago

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