A child gets a half dollar from the Tooth Fairy for losing a tooth, and the child excitedly begins tossing the coin, noticing that it lands heads-up the first 6 times they toss it. The child exclaims that the coin must be either magic or somehow weighted because it didn't land tails up for half of the tosses. Explain, with an argument rooted in the Law of Large Numbers, whether the child is right to conclude that the coin is magic or unfairly weighted.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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A child gets a half dollar from the Tooth Fairy for losing a tooth, and the child excitedly begins tossing the coin, noticing that it lands heads-up the first 6 times they toss it. The child exclaims that the coin must be either magic or somehow weighted because it didn't land tails up for half of the tosses. Explain, with an argument rooted in the Law of Large Numbers, whether the child is right to conclude that the coin is magic or unfairly weighted. 

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