Probability of Blue Ball from 10-Ball Urn

[needhelp83]

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?

 

[Dick]

What probability would you assign before Michael takes out one of the balls?

 

[D H]

To add to Dick's post: Does Michael's action add any new information that would let you change that initial assignment?

 

[needhelp83]

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

 

[D H]

A red ball? The urn contains only blue and green balls.

 

[LCKurtz]

Dude! You missed that this is a magic show.

 

[needhelp83]

I apologize, I meant blue

 

[D H]

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.