Chapter 1: Problem 3
A coin is to be tossed as many times as necessary to turn up one head. Thus the elements \(c\) of the sample space \(\mathcal{C}\) are \(H, T H, T T H, T T T H\), and so forth. Let the probability set function \(P\) assign to these elements the respec- tive probabilities \(\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}\), and so forth. Show that \(P(\mathcal{C})=1 .\) Let \(C_{1}=\\{c\) : \(c\) is \(H, T H, T T H, T T T H\), or \(T T T T H\\} .\) Compute \(P\left(C_{1}\right) .\) Next, suppose that \(C_{2}=\) \(\left\\{c: c\right.\) is TTTTH or TTTTTH\\}. Compute \(P\left(C_{2}\right), P\left(C_{1} \cap C_{2}\right)\), and \(P\left(C_{1} \cup C_{2}\right)\).
Short Answer
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Key Concepts
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