Probability of picking one of several balls of one of two colors

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Discussion Overview

The discussion revolves around calculating the probability of selecting a yellow ball from a bag containing yellow and green balls, specifically addressing two scenarios: randomly choosing a ball and choosing a ball after discarding two others. The focus is on understanding the implications of discarding balls without knowing their colors.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant calculates the probability of selecting a yellow ball in the first scenario as 4/6 or 2/3.
  • Another participant suggests that for the second scenario, assuming the colors of the discarded balls are unknown simplifies the problem, leading to the same probability of 2/3.
  • A third participant expresses confusion about how the probability remains 2/3 in the second scenario and seeks clarification.
  • A later reply reinforces that if the colors of the discarded balls are not considered, the reasoning for the second scenario mirrors that of the first.

Areas of Agreement / Disagreement

There is no consensus on the reasoning behind the probability for the second scenario, as some participants agree with the simplification while others express confusion and seek further explanation.

Contextual Notes

The discussion does not resolve the assumptions regarding the impact of discarding balls on the overall probability calculation, particularly in terms of the unknown colors of the discarded balls.

sara_87
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An bag contains four yellow balls and two green balls. Find the probability of getting a yellow
ball if you. . .
(a) . . . randomly choose a ball from the urn.
(b) . . . randomly choose and discard two balls and then choose a third.

i know how to do part a..it's just 4/6 = 2/3
but for part b, i can't do it because there will be three cases: discarding 2 yellow, discarding 2 green or discarding 1 yellow and 1 green but i should only get 1 answer
?
 
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For part (b) you will find it easier to do if you assume that you DON'T look at the 2 balls you discarded. In this way you will see the answer is still 2/3.
 
but how did you get 2/3 ?
i tried to work it but couldn't know how??
 
If you don't know what the 2 discarded balls are, then the reasoning for (b) is identical to the reasoning for (a).
 

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