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Chapter 3: Q.3.31 (page 111)
There is a percent chance that event will occur. If does not occur, then there is a percent chance that will occur. What is the probability that at least one of the events will occur?
The probability that at least one of the events or will occur
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A total of percent of the women and percent of the men who took a certain鈥渜uit smoking鈥� class remained nonsmokers for at least one year after completing the class. These people then attended a success party at the end of the year. If percent of the original class was male,
(a) what percentage of those attending the party were women?
(b) what percentage of the original class attended the party?
(a) An urn containswhite and black balls. The balls are withdrawn one at a time until only those of the same color are left. Show that with probability , they are all white. Hint: Imagine that the experiment continues until all the balls are removed, and consider the last ball withdrawn.
(b) A pond containsdistinct species of fish, which we will call the Red, Blue, and Greenfish. There are Red, Blue, and Greenfish. Suppose that the fish are removed from the pond in random order. (That is, each selection is equally likely to be any of the remaining fish.) What is the probability that the Redfish are the first species to become extinct in the pond?
Hint: Write , and compute the probabilities on the right by first conditioning on the last species to be removed.
A total of percent of the voters in a certain city classify themselves as Independents, whereas percent classify themselves as Liberals and percent say that they are Conservatives. In a recent local election, percent of the Independents, percent of the Liberals, and percent of the Conservatives voted. A voter is chosen at random. Given that this person voted in the local election, what is the probability that he or she is
(a) an Independent?
(b) a Liberal?
(c) a Conservative?
(d) What percent of voters participated in the local election?
An urn has r red and w white balls that are randomly removed one at a time. Let be the event that the ith ball removed is red. Find
a).
b).
c).
In Example, what is the probability that someone has an accident in the second year given that he or she had no accidents in the first year?
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