In this problem, Greg states that pulling a red marble and keeping it, then pulling a blue marble is considered a case of independent events. Can somebody elaborate further on why? How can they be independent if the probability for pull 2 is inherently changed? Greg says to treat it like a new bag of marbles but I don’t understand how they’d still be considered independent on a GRE question?
Hi, thanks for your reply. I understand the equal probabilities between pulling a certain ball 1st vs. 5th, etc. From reviewing the thread, I am not quite sure that answers my question as to how the events are considered independent. Is that fact that the probability doesn’t change proof of the independence of events, or am I missing some sort of connection? Thanks!
Yes, events A and B are independent if P(B given A occurred) = P(B) (A happening does not change B’s likelihood → B is exactly as likely to happen whether A happens or not). The same goes if you swap the letters A and B above in the definition (i.e. B happening does not change A’s likelihood of happening).
If the probability of one event changes when the other occurs, then those events are not independent (aka dependent).
Thanks for your response. The technicality I am hung up on is this - in this case, isn’t the probability of one event changing when the other occurs, given that the total available number of outcomes is changing? If A occurs, probability of B changes from 5/10 to 5/9, correct?
Those should not be independent events because the probability changes. Selecting a red increases the likelihood of a blue on 2nd try. Where is that slide? We should correct it
If you did replace the marbles after drawing it, then those events would be independent.
This is under the independent events video on PrepSwift, towards the end of the video.