Solution: Probability A fair coin is tossed repeatedly. The probability that the first
Chapter 9, Problem 79(choose chapter or problem)
Probability A fair coin is tossed repeatedly. The probability that the first head occurs on the nth toss is given by \(P(n)=\left(\frac{1}{2}\right)^{n}, \text { where } n \geq 1\).
(a) Show that \(\sum_{n=1}^{\infty}\left(\frac{1}{2}\right)^{n}=1\).
(b) The expected number of tosses required until the first head occurs in the experiment is given by
\(\sum_{n=1}^{\infty}\left(\frac{1}{2}\right)^{n}\).
Is this series geometric?
(c) Use a computer algebra system to find the sum in part (b).
Text Transcription:
P(n)=(1/2)^n, where n geq 1
Sum_n=1^infinity (1/2)^n = 1
Sum_n=1^infinity (1/2)^n
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