please type in your hand clearly so I can understand the formula and explanation thank you  Consider the following game. A fair coin is flipped until the first tail appears; we win $2 if it appears on the first toss, $4 if it appears on the second toss, and in general  if it first occurs on the k-th toss. Let the random variable X denote our winning. How much should we have to pay in order for this to be a fair game? Note: A fair game is one where the difference between the ante and E(X) is 0

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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please type in your hand clearly so I can understand the formula and explanation thank you 

Consider the following game. A fair coin is flipped until the first tail appears; we win $2 if it appears on the first toss, $4 if it appears on the second toss, and in general  if it first occurs on the k-th toss. Let the random variable X denote our winning. How much should we have to pay in order for this to be a fair game? Note: A fair game is one where the difference between the ante and E(X) is 0  

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