I have a doubt regarding the Data analysis progress quiz #9 (foundational quiz). If I’m not mistaken, questions 6 and 12 should have the same approach - the probability being the same irrespective of the draw, but question 12 has taken a different approach. I’m now confused about which approach is correct, as I can’t distinguish between the questions.
Well, for a start, the first question constrains the types of pulls you have, which the second question doesn’t seem to do. For example, in the first question, you know for sure that the first two pulls aren’t peaches, whereas nothing is stopping the second and third balls from being green simultaneously.
It looks like the second question is clear that the balls are drawn without replacement. However, the first question states that the candies are all replaced if he cannot find a peach one. i believe this is what makes the question different, as you may have to solve with the concept of replacement in mind? hopefully the gregmat team can shed some light on this as well.
It isn’t the replacement part that’s confusing! It’s the part where the peach, or ball, has been drawn out 2nd or 6th.
(replacement does not affect the probability of the draw, which is the concept I imagined should be tested in both of these, but it only tested in the ball question)
As mentioned, the reason you aren’t just finding the probability of peach candies is the phrase:
until he finds a peach one, at which point he stops.
Had this not been there, you could certainly treat it like Question 6, because a bijection exists even though we’re trying to transition from a uniform probability to a non-uniform one.
Basically, Question 6 has no restriction requiring the first 5 balls NOT be green, whereas Question 12 requires that the first two candy pieces are NOT peaches.
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ah that makes sense! Thank you!