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Say I have a bag of 5 balls. I know there is some mixture of red and black balls in the bag. I pull out 4 balls and replace as follows: Red, Black, Red, Black.

Can I assume there is a 50% chance the next ball I pull out is Red if I have no other information about the ball.

What if I had not yet pulled any balls out of the bag?

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    $\begingroup$ You can assign prior probabilities as you see fit to a given situation, but if you want to adopt a general principle like "probabilities I am ignorant of should be assigned the value 1/2" you can rapidly arrive at inconsistencies. $\endgroup$
    – Glen_b
    Nov 29, 2018 at 4:57
  • $\begingroup$ It depends on what it costs you to be wrong. After all, it is mathematically provable that the chance cannot be 50%! $\endgroup$
    – whuber
    Nov 29, 2018 at 15:09

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