This is another example of how to use limit to distinguish answer.
First, (A) and (E) are wrong since they do not depend on
.
Next, as
is large, the probrability that none of the helium atoms in a certain volume is extremely low, since more atoms tends to spread over the place. So, (D) is wrong since as N is large, (D) goes to one.
Now, let
. That is, consider only one atom. Now, the problem is easy. The probability that an atom will be in a certain volume is proportional to the volume itself. So, the probability that one atom
will not be in a
cubic meter volume is then
This makes (B) wrong. The only answer left is (C).
The correct answer is (C), and 36 out of 100 people got the right answer.
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