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We roll a dice 10 times. What is a probability of obtaining a 6 in a first roll (event A) if we obtain 6 in all next 9 rolls (event B). Is it that simple that $P(A | B) = \frac{P(A \cap B)}{P(B)} = \frac{1}{6}$? This excersise is in the part about Bernoulli scheme, so I'm wondering if I'm doing it right...

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Yes, it’s that simple: the first roll does not depend in any way on the other rolls. – Brian M. Scott Mar 9 '13 at 23:47
Assuming independence of rolls: yes, the probability to roll 6 is $\frac{1}{6}$ – Alex Mar 9 '13 at 23:58

Yes, those events are following one another and are independent, therefore the probability of getting a 6 for the first roll is $\frac{1}{6}$.

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