What is the probability that the first toss was the tail?

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Homework Help Overview

The problem involves calculating the probability of the first toss being a tail given that a coin is tossed three times and lands heads exactly twice. The subject area is probability theory, specifically focusing on conditional probability.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss different methods of solving the problem, including manual solutions and the use of notation. There are questions about the appropriate notation and examples of its application. Some participants consider the outcomes of the coin tosses and whether to distinguish between identical results.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and questioning the methods and assumptions involved. Some guidance on using conditional probability has been suggested, but there is no explicit consensus on the solution or approach yet.

Contextual Notes

There is mention of avoiding certain methods, such as nCr, and a participant expresses uncertainty about the answer, indicating a lack of complete information or clarity on the problem setup.

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Homework Statement


A coin is tossed 3 times and you note that the coin lands heads exactly twice. What is the probability that the first toss was the tail?


The Attempt at a Solution



I've solved the problem manually not using notation.


So I want to try to solve with notation?

Thanks
 
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I am not familiar with the notation you speak of, can you give me an example of what you're asking for?
 


p(the coin landed tail)=.5
 


Without using nCr
But Conditional Prbability
 


Well what answer did you get? :)
 


i also learning probability and just to ask those who have completed this, is the answer 1/6 ?
 


Tricky! I'm thinking of a manual solution like this:
The possible outcomes are HHT, HTH, THH.
BUT I'm wondering if I need to distinguish between the two H's so it is
HhT, hHT,HTh,hTH,THh,ThH
 

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