Yes, it is conditional probability. However, if the question asked you to use combinations or permutations to solve the problem, then you would be expected to solve it in that manner rather than using a conditioning argument. Therefore, if you are upset because you were not given credit for the correct answer, that would be the reason. I'm not a big fan of penalizing right answers because of how the solution is derived.
Tom K.
tutor
A combination answer would be P(2nd is blue|first is blue) = P(2 blues)/P(first blue)
P(2 blues) = C(4,2)/C(7,2) = 6/21 = 2/7
P(first blue) = 4/7
P(2nd is blue|first is blue) = 2/7/(4/7) = 1/2
Without knowing the instructions given, I can't really say what the right answer is.
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12/19/20
Tom K.
tutor
If your answer was not 1/2, then the problem was with your use of conditional expectation. I am assuming that your answer was based on 3 blue balls remaining out of 6, so the probability is 3/6 = 1/2.
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12/19/20
Stela P.
can you provide the solution for the same?12/19/20