Chapter 7: Q47E (page 494)
Question: When \(m\) balls are distributed into \(n\) bins uniformly at random, what is the probability that the first bin remains empty?
Answer
The resultant answer is\({\left( {\frac{{n - 1}}{n}} \right)^m}\).
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Question: What is the probability that a five-card poker hand does not contain the queen of hearts?
Question:Ramesh can get to work in three different ways: by bicycle, by car, or by bus. Because of commuter traffic, there is a\({\bf{50}}\% \)chance that he will be late when he drives his car. When he takes the bus, which uses a special lane reserved for buses, there is a\({\bf{20}}\% \)chance that he will be late. The probability that he is late when he rides his bicycle is only\({\bf{5}}\% \). Ramesh arrives late one day. His boss wants to estimate the probability that he drove his car to work that day.
a) Suppose the boss assumes that there is a\({\bf{1}}/{\bf{3}}\)chance that Ramesh takes each of the three ways he can get to work. What estimate for the probability that Ramesh drove his car does the boss obtain from Bayes’ theorem under this assumption?
b) Suppose the boss knows that Ramesh drives\(3{\bf{0}}\% \)of the time, takes the bus only\({\bf{10}}\)% of the time, and takes his bicycle\({\bf{60}}\% \)of the time. What estimate for the probability that Ramesh drove his car does the boss obtain from Bayes’ theorem using this information?
Question: To Determine the probability that a five-card poker hand contain exactly one ace.
Question: Suppose that the probability that \(x\) is in a list of n distinct integers is\(\frac{2}{3}\) and that it is equally likely that \(x\) equals any element in the list. Find the average number of comparisons used by the linear search algorithm to find \(x\) or to determine that it is not in the list.
Question: What is the probability that a five-card poker hand contains cards of five different kinds and does not contain a flush or a straight.
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