Chapter 7: Q9E (page 451)
Question: What is the probability that a five-card poker hand does not contain the queen of hearts?
Answer
The probability that a five-card poker hand does not contains the queen of hearts is
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Question: Would we reject a message as spam in Example 4
a) using just the fact that the word “undervalued” occurs in the message?
b) using just the fact that the word “stock” occurs in the message?
Question: What is the probability that the sum of the numbers on two dice is even when they are rolled?
Question: Prove Theorem \(2\), the extended form of Bayes’ theorem. That is, suppose that \(E\) is an event from a sample space \(S\) and that \({F_1},{F_2},...,{F_n}\) are mutually exclusive events such that \(\bigcup\nolimits_{i = 1}^n {{F_i} = S} \). Assume that \(p\left( E \right) \ne 0\) and \(p\left( {{F_i}} \right) \ne 0\) for \(i = 1,2,...,n\). Show that
\(p\left( {{F_j}\left| E \right.} \right) = \frac{{p\left( {E\left| {{F_j}} \right.} \right)p\left( {{F_j}} \right)}}{{\sum\nolimits_{i = 1}^n {p\left( {E\left| {{F_i}} \right.} \right)p\left( {{F_i}} \right)} }}\)
(Hint: use the fact that \(E = \bigcup\nolimits_{i = 1}^n {\left( {E \cap {F_i}} \right)} \).)
Question: What is the probability that a fair die never comes up an even number when it is rolled six times?
Question: Suppose thatandare events in a sample space and, and . Find.
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