Probability of Blue Ball from 10-Ball Urn

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Homework Help Overview

The discussion revolves around a probability problem involving an urn containing 10 balls, specifically 5 blue and 5 green. The scenario involves a participant, Michael, drawing a ball at random without revealing which color was drawn, prompting questions about the probability of subsequently drawing a blue ball.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the initial probability assignment of drawing a blue ball, questioning whether Michael's action introduces new information that could alter this probability. There is also exploration of how the knowledge of the drawn ball affects future probability assessments.

Discussion Status

The discussion is active, with participants exploring various interpretations of the problem. Some have provided initial probability estimates, while others are questioning assumptions and clarifying the conditions of the problem. There is no explicit consensus yet, but the conversation is delving into the implications of Michael's draw on the overall probability assessment.

Contextual Notes

Participants are navigating the constraints of the problem, including the specific colors of the balls in the urn and the implications of Michael's action on the probability calculations. There is a noted confusion regarding the mention of a "red ball," which is not part of the problem's setup.

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Stuck on this question:

Suppose you know that there is an urn with 10 balls inside: 5 blue and 5 green. You believe each ball is equally likely to be drawn from the urn. Michael takes out one of the balls at random but doesn't show you which one. What probability should you assign to pulling out a blue ball from urn?
 
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What probability would you assign before Michael takes out one of the balls?
 
To add to Dick's post: Does Michael's action add any new information that would let you change that initial assignment?
 
Alright, so the initial probability for Michael is .5 because it is either blue or green. Now Michael's action makes you believe probability of pulling out red ball is 4/9
 
A red ball? The urn contains only blue and green balls.
 
Dude! You missed that this is a magic show.
 
I apologize, I meant blue
 
How can Michael's action possibly bias the answer in favor of green?

Michael will draw a blue ball or green ball with equal probabilities, 1/2. Suppose you know he draws a blue ball. What is the probability the next ball will be blue? Now suppose you know he draws a green ball. Once again, what is the probability the next ball will be blue?

You don't know what Michael drew, but there is a way to combine those probabilities.
 

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