Elementary Statistics (12th Edition)

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

Chapter 5 - Discrete Probability Distributions - 5-3 Binomial Probability Distributions - Basic Skills and Concepts: 14

Answer

a) 0.0081 b) MMXX, MXMX, MXXM, XMXM,XMMX, XXMM, 0.0081. c)0.0486

Work Step by Step

a) The probability of guessing a number correctly is $\frac{1}{10}$ and of gussing incorrectly is $\frac{9}{10}$. ALso, these selections are independent. Therefore the probability:$P(MMXX)=\frac{1}{10}\cdot \frac{1}{10} \cdot \frac{9}{10} \cdot \frac{9}{10}=0.0081.$ b) The good possibilities are MMXX, MXMX, MXXM, XMXM,XMMX, XXMM and each of them have the same probability of 0.0081. c) Using b), the probability of getting exactly 2 matching digits out of 4 is $6\cdot 0.0081=0.0486$.
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