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What are the chances of this happening?

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In a pool of questions, there are undoubtedly the dirt simple ones and the more difficult ones. Chances are the 3 questions will be a simple one, a moderately difficult one and a fairly hard one. Chances also are that you will choose to skip learning the hard one - so there is a fairly good chance a question is selected that you didn't study.
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Assuming every question is equally likely there are nCr(50,3) = 50\*49\*48/(3\*2) = 19'600 possibilities.

Assuming, one of the choices has to be the question, there are nCr(49,2)\*1= 49\*48/2= 1176 possibilities.

Now, these two events are assumed to be independent ie the questions of the first exam don't influence the questions of the second exam.

This means, the probability of this event happening twice in a row is equal to the probability of it happening once squared.

The probability of this happening is

>P(x) = 1176/19600 => P(x)\^2= (1176/19600)\^2=0.0036 = 0.36%

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