Chapter 7: Q8E (page 451)
Question: What is the probability that a five-card poker hand contains the ace of hearts?
Answer
The probability that a five-card poker hand contains the ace of heart is
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Question: Let E be the event that a randomly generated bit string of length three contains an odd number of 1s, and let F be the event that the string starts with 1. Are E and F Independent?
Question: Find the probability of selecting exactly one of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding
(a) 40.
(b) 48.
(c) 56.
(d) 64.
Question: What is the expected number of heads that come up when
a fair coin is flipped 10 times?
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: What is the probability that a five-card poker hand contains a royal flush, that is, the , jack, queen, king and ace of one suit.
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