Alan

I interpreted this question as meaning what is the probability that Alex will catch the train.  

Strictly interpreted, the question requires the probability that the train is already in the station when Alex arrives, which is how Melody and civonamzuk have interpreted it (in my interpretation Alex could be waiting for some time before the train arrives!).

For the alternative probability I get 11/72 = 0.153.  

(On my diagram imagine a line running from (0,0) to (60, 60).  Alex has to arrive in the band between this line and the blue line, the area of which is a fraction 0.153 of the red box area.)

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Chris is correct.  I didn't account for the C(91,1) and C(91,90) values.  

I actually wrote a little program that ran through values of n and, for each n, tried values of k from 1 to n to find those combinations for which C(n,k) = 91.  However, I stopped short of n = 91.  Silly!

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I looked it up!

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By definition one gram-mole of a substance contains (approximately) 6x10²³ atoms (this is known as Avogadro's number or Avogadro's constant).

The atomic weight of silicon is 28, so Avogadro's number of silicon atoms weigh 28 grams. Therefore 1 atom of silicon weighs (28/Avogardo's number) grams.

Do a search on Avogadro's number to find a more accurate value than I've used here; and search on atomic weight of silicon to find the value of 28.

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The circumference.

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I should have said the probability that Alex catches the train is given by the area in the red box below and to the right of the blue line divided by the area of the red box.

Perhaps this graph will help:

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I think you could probably do 1/2 - 1/[(n+1)(n+2)] on a hand-held without too much difficulty.

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normpdf calculates the probability density function values for a normal distribution of given mean and standard deviation.

For example, if we have a normal distribution with mean 10 and standard deviation 3 and we want to know the value of the probability density at 12, then normpdf(12,10,3) = 0.106483   (at least, that's how it's done on the TI-Nspire calculator).

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