Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 39 - Wave Functions and Uncertainty - Exercises and Problems - Page 1174: 2

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Work Step by Step

$$\color{blue}{\bf [a]}$$ Here is the table of the possible outcomes of the 3 coins experiment. \begin{array}{|c|c|c|} \hline \text{Coin A} & \text{Coin B} & \text{Coin C} \\ \hline H & H & H \\ \hline H & H & T \\ \hline H & T & H \\ \hline H & T & T \\ \hline T & H & H \\ \hline T & H & T \\ \hline T & T & H \\ \hline T & T & T \\ \hline \end{array} $$\color{blue}{\bf [b]}$$ From the table above, it is obvious that we have 8 rows that represent the 8 possible outcomes. We can get two heads and one tail 3 times out of 8. Thus, the probability of getting two heads and one tail is $$P_{\rm HHT}=\dfrac{3}{8}\times 100\%=\color{red}{\bf 37.5}\%$$ $$\color{blue}{\bf [c]}$$ From the table above, the probability of getting at least two is $$P_{\text{HH at least} }=\dfrac{4}{8}\times 100\%=\color{red}{\bf 50}\%$$
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