2. You have two coins, one that comes up heads 50% of the time and one that comes up heads 70% of the time. A friend of yours who wants to win some bets borrows what he thinks is your 70% coin to use on some unsuspecting people. Before using the coin, however, he decides to try it out on himself by tossing it 10 times. He decides that if heads come up 8 or more times out of 10, he will conclude that you really did give him the biased (70%) coin. a) If, in fact, you gave him the fair (50%) coin, what is the probability that he will incorrectly conclude that you gave him the biased coin? b) If, in fact, you gave him the biased coin, what is the probability that he will incorrectly conclude that you gave him the fair coin? c) Suppose he tossed the coin 25 times and decided to use α ≤ .05 to create a new decision rule. What is the probability that he would now incorrectly conclude that you gave him the fair coin if, in fact, you gave him the biased coin? Answers: A)0.055 B)0.617 C)0.488

2. You have two coins, one that comes up heads 50% of the time and one that comes up heads 70% of the time. A friend of yours who wants to win some bets borrows what he thinks is your 70% coin to use on some unsuspecting people. Before using the coin, however, he decides to try it out on himself by tossing it 10 times. He decides that if heads come up 8 or more times out of 10, he will conclude that you really did give him the biased (70%) coin. a) If, in fact, you gave him the fair (50%) coin, what is the probability that he will incorrectly conclude that you gave him the biased coin? b) If, in fact, you gave him the biased coin, what is the probability that he will incorrectly conclude that you gave him the fair coin? c) Suppose he tossed the coin 25 times and decided to use α ≤ .05 to create a new decision rule. What is the probability that he would now incorrectly conclude that you gave him the fair coin if, in fact, you gave him the biased coin? Answers: A)0.055 B)0.617 C)0.488

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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