Suppose you have two biased coins, but you don't know which coin is which. Coin 1 comes up heads with probability 3/4, while coin 2 comes up heads with probability 1/3. Suppose you pick a coin at random and flip it. Let Ci denote the event that coin i is picked . Let H and T denote the possible outcomes of the flip. (a) Draw a tree diagram for the experiment. (b) Given that the outcome of the flip is a head, what is P[C2|H], the probability that you picked the second coin? (c) Given that the outcome is a tail, what is the probability P[C1|T] that you picked the first coin?

Suppose you have two biased coins, but you don't know which coin is which. Coin 1 comes up heads with probability 3/4, while coin 2 comes up heads with probability 1/3. Suppose you pick a coin at random and flip it. Let Ci denote the event that coin i is picked . Let H and T denote the possible outcomes of the flip. (a) Draw a tree diagram for the experiment. (b) Given that the outcome of the flip is a head, what is P[C2|H], the probability that you picked the second coin? (c) Given that the outcome is a tail, what is the probability P[C1|T] that you picked the first coin?

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Description: Suppose you have two biased coins, but you don't know which coin is which. Coin 1comes up heads with probability 3/4, while coin 2 comes up heads with probability 1/3.Suppose you pick a coin at random and flip it. Let Ci denote the event that coin i

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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

Suppose you have two biased coins, but you don't know which coin is which. Coin 1
comes up heads with probability 3/4, while coin 2 comes up heads with probability 1/3.
Suppose you pick a coin at random and flip it. Let Ci denote the event that coin i is
picked . Let H and T denote the possible outcomes of the flip.
(a) Draw a tree diagram for the experiment.
(b) Given that the outcome of the flip is a head, what is P[C2|H], the probability that you
picked the second coin?
(c) Given that the outcome is a tail, what is the probability P[C1|T] that you picked the
first coin?

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