IMPORTANT NOTE: Please provide full detailed justifications. (i) A bag contains one trick coin that always shows heads when flipped, and nine fair coins (that show heads with probability 12 and tails with probability 12 when flipped). A coin is selected uniformly at random from the bag and flipped four times. What is the probability that the coin selected was the trick coin, given that it shows heads all four times? (ii) A bag contains n coins, one of which is a trick coin and the rest of which are fair (the coins are as described in (i)). A coin is selected uniformly at random from the bag and flipped k times. The coin shows heads all k times and, given this, you calculate that there is an exactly 50% probability that the coin selected was the trick coin. What is n ? (Write your answer as an expression in terms of k.)
IMPORTANT NOTE: Please provide full detailed justifications. (i) A bag contains one trick coin that always shows heads when flipped, and nine fair coins (that show heads with probability 12 and tails with probability 12 when flipped). A coin is selected uniformly at random from the bag and flipped four times. What is the probability that the coin selected was the trick coin, given that it shows heads all four times? (ii) A bag contains n coins, one of which is a trick coin and the rest of which are fair (the coins are as described in (i)). A coin is selected uniformly at random from the bag and flipped k times. The coin shows heads all k times and, given this, you calculate that there is an exactly 50% probability that the coin selected was the trick coin. What is n ? (Write your answer as an expression in terms of k.)
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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Transcribed Image Text:IMPORTANT NOTE: Please provide full detailed
justifications.
(i) A bag contains one trick coin that always shows
heads when flipped, and nine fair coins (that show
heads with probability 12 and tails with probability
12 when flipped). A coin is selected uniformly at
random from the bag and flipped four times. What
is the probability that the coin selected was the
trick coin, given that it shows heads all four times?
(ii) A bag contains n coins, one of which is a trick
coin and the rest of which are fair (the coins are as
described in (i)). A coin is selected uniformly at
random from the bag and flipped k times. The coin
shows heads all k times and, given this, you
calculate that there is an exactly 50% probability
that the coin selected was the trick coin. What is n ?
(Write your answer as an expression in terms of k.)
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