Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 4 - Probability - 4-6 Counting - Basic Skills and Concepts: 28

Answer

a) $\frac{1}{10,000,000,000,000,000}$ b)$\frac{1}{1,000,000,000,000}$ c) $\frac{1}{100,000,000}$

Work Step by Step

a)By using the fundamental counting rule(knowing that there are 10 digits) we can get the number of possibilities: $10\cdot 10\cdot... \cdot 10=10^{16}=10,000,000,000,000,000.$. We also know that $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$, therefore $P=\frac{1}{10,000,000,000,000,000}$. b) By using the fundamental counting rule(knowing that there are 10 digits) we can get the number of possibilities: $10\cdot 10\cdot... \cdot 10=10^{12}=1,000,000,000,000.$. We also know that $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$, therefore $P=\frac{1}{1,000,000,000,000}$. c)By using the fundamental counting rule(knowing that there are 10 digits) we can get the number of possibilities: $10\cdot 10\cdot... \cdot 10=10^{8}=100,000,000.$. We also know that $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$, therefore $P=\frac{1}{100,000,000}$.
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