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There is an urn with 55 green, 66 red, and 44 yellow balls. You pick 44 balls without replacement (that is, without putting the balls back after each pick). Let A� be the event you pick 22 green balls and B� be the event you pick 22 yellow balls. Find P(A|B)�(�|�) and P(B|A)�(�|�).
For this question from Math Challenge II B, week 9, I'm confused if there are no intersections between events A and B, how do we solve this problem?
Remember that you're picking 4 balls without replacement.
Thus, A = "you pick 2 green balls" = "you pick 2 green balls and 2 other (non-green balls)". A similar thing happens for B. This means that actually there is an intersection between the two events.
Further, note that any two events have an intersection, it just could be the case that the intersection is the empty set (with probability 0). Hence, if the question was asked where you just picked 2 balls, P(A|B) and P(B|A) would both be 0.
Hope this helps!
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