**Coin Flip Probability Problem**1. **What is the probability that the flip lands on heads?**2. **Given that the flip lands on heads, what is the probability that you picked one of the fair coins?**---In this problem, you're asked to determine the probability of a coin flip resulting in heads and then, given this outcome, the probability of having selected one of the fair coins. This involves understanding concepts of probability, including conditional probability, which assesses the likelihood of an event occurring, given that another event has already occurred. Say you have three coins in your pocket. Two of the coins are fair coins (have a head side and a tail side, and each side is equally likely), and you have one coin that both sides are heads. Label the fair coins C₁ and C₂, while the unfair two-headed coin is labeled as C₃.You are going to reach into the pocket and randomly pick a coin (each coin has 1/3 chance of being picked), and then you are going to flip that coin.Given that the flip lands on heads, what is the probability that you picked the two-headed coin?

Answered: Say you have three coins in your…

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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Suppose I flip a fair coin n = 20 times. A psychic tries to predict the outcome before each flip. Three researchers have different ideas about the psychic's ability. There is Sydney, the Skeptic (S), who thinks the psychic's success rate is between 49% and 51%. There is Morgan, the Mark, M, who thinks that the psychic's success rate is 80%. And there is Carter, the Cynic (C), who thinks the psychic's success rate is 10%. Specifically: S+ 0 ~ U(.49, .51) M + 0 = .80 C0 = .10 %3D In all cases, assume the number of successful predictions follows a binomial distribution with success rate 0. Usek for the number of successes and n for the number of trials. Given all that: Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Carter over Morgan. Call that Bayes factor Bc:M Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Morgan over Sydney. Call that Bayes factor BM:S Determine the formula for the Bayes factor (a.k.a., likelihood…
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