[BruceZ]

I thought of a shortcut to c and d where you only need to compute 2 terms. It is an approximation, but it should be very close. You should have 13 or more approximately 50% of the time, and 12 or less approximately 50% of the time. So if you want the probability of 10 or less, compute the probability of exactly 11 and 12, and subtract this from 50%. Similarly for 15 or more, compute the probability of exactly 13 and 14 and subtract this from 50%. Perhaps this is why the problem picked the numbers it did. It would be exact if the probability of red or black was exactly 50%. There is also an approximate formula for the binomial "tail" which you may have been given.

If you need an exact answer you could a) compute 11 terms 0-10 by hand and add them together for d, then compute 4 more terms 11-14 and subtract terms 0-14 from 1 for part c b) write a program or spreadsheet to do this c) use a table of the binomial "tail" if you have one d) use a table of the binomial disribution if you have one that applies to this case, and add the right numbers togther from the table.