Question: Suppose you are given a bag containing n unbiased coins. You are told that n 1 of these coins are normal, with heads on

Suppose you are given a bag containing n unbiased coins. You are told that n — 1 of these coins are normal, with heads on one side arid tails on the other, whereas one coin is a fake, with heads on both sides.

a. Suppose you reach into the bag, pick out a coin uniformly at random, flip it, and get a head. What is the (conditional) probability that the coin you chose is the fake coin?

b. Suppose you continue flipping the coin for a total of k times after picking it and see k heads. Now what is the conditional probability that you picked the fake coin?

c. Suppose you wanted to decide whether the chosen coin was fake by flipping it k times. The decision procedure returns FAKE if all k flips come up heads, otherwise it returns NORMAL. What is the (unconditional) probability that this procedure makes an error?

Step by Step Solution

★★★★★

3.37 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a There are n ways to pick a coin and 2 outcomes for each flip although with the fake coin the ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

21-C-S-A-I (204).docx

120 KBs Word File

Students Have Also Explored These Related Artificial Intelligence Questions!

Suppose you are given these hypotheses: H0: 25, H1: > 25; and that the standard deviation from a sample of 100 is 2.4. What is the power of the test at a 5% level of significance if the...

Suppose you are given n different springs. In which order should you connect them to unit masses so that the mass-spring chain vibrates the fastest? Does your answer depend upon the relative sizes of...

Given a bag containing 2 red marbles, 2 blue marbles, 3 yellow marbles, and 1 green marble, find the following: 1. The probability of choosing a blue marble from the bag 2. The probability of...

1 Suppose you are given a bag containing n unbiased coins. You are told that n 1 of these coins are normal, with heads on one side and tails on the other, whereas one coin is a fake, with heads on...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

Math 221 Discrete Mathematics UOPX Make sure all of the are fresh work with proper citation APA format, no used work will be accepted thanks so much. To be substantive, in addition to meeting the...

Hi, math experts. I am recently learning from Pattern Recognition and Machine Learning, Chris Bishop. Please provide a detailed explainations briefly for the following sections. 1. Section 1.2.2...

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

1 2.3 Definition of a Discrete Probability Function Definition: Let S be a discrete sample space from some experiment. A function P, defined on all events in S, is said to be a probability function...

In 2018, which of the following children would have income taxed at trust and estate rates? a. A 9-year-old child with salary income of $1,000 b. A 12-year-old child with net unearned income of...

How do you find the solution using the method for the exact equation? dy/dx = x/y y(0) = 1

Florida Real Estate license exam 2 0 2 5 as an agent a broker is employed by and acts on behalf of whom

Deborah Daughetee consumed multiple bags of microwave popcorn daily for approximately 5 years. Deborah recalled eating more than 10 different brands of buttered popcorn. After removing a bag of...

Jon Summervold purchased a remote controlled toy watercraft from the Walmart store located in Aberdeen, South Dakota. The plaintiff sued Wal Mart, Inc. for alleged defective design and failure to...

The Wolf Appliance Co. provides a 120-day parts-and-labor warranty on all merchandise it sells. Wolf estimates the warranty expense for the current period to be $2,450. During the period a customer...

The following process is used by the Otis Company to process cash receipts. Describe the positive and negative elements of this process. Include operational, information, and control issues. What...

You work for Nokia in its global cell phone group. You have been made project manager for the design of a new cell phone. Your supervisors have already scoped the project so you have a list showing...

A service operation is offered seven days per week. Demand for the service is such that four workers are required throughout the week. Work rules require that each worker be given two consecutive...

The two axes of an xy positioning table are each driven by a stepping motor connected to a lead screw with a 10:1 gear reduction. The number of step angles on each stepping motor is 20. Each lead...

Write the part program to drill the holes in the part shown in Figure P7.26. The part is 12.0 mm thick. Cutting speed = 100 m/min and feed = 0.06 mm/rev. Use the lower left corner of the part as the...

14.15 Prove that the three axioms of probability are necessary for rational behavior in betting situations, as shown by de Finetti

15.6 Is probabilistic reasoning monotonic or nonmonotonic? Do these concepts even apply to probabilities?

16.2 Tickets to the state lottery cost $1. There are two possible prizes: a $10 payoff with probability 1/50, and a $1,000,000 payoff with probability 1/2,000,000. What is the expected monetary value...

9. A study of 99 dental hygienists were found to have an exposure to mercury vapors at an average of 0.08 mg/m3 (o=0.005) over a 10-hour work shift. The regulatory limit for mercury vapors is 0.05...