Probability of Snow in New York In New York, snow is reported 25% of days in February.  If this trend continues, what is the probability that it will snow exactly 9 days this coming February and is not a leap year?
Solve this problem by using 
First)  The approximation of the binomial distribution 
Second) The Binomial Distribution
How would I apply the Binomial Distribution and approximate distribution? I am having difficulty extracting the info from the problem.
So far I have the following
p = .25
q = .75
n = 28 days
k = 9 
Would I apply that to C(n,k)(p^k)(q^n-k)?
 A: Yes. Under the assumption that the binomial distribution is applicable (i.e. it snows on each day in February with probability $25\%$, independent of other days) the probability of exactly $9$ days with snow is
$$ \binom{28}{9} (.25)^9 (.75)^{19}. $$
There are $\binom{28}{9}$ ways to choose the $9$ days, the probability that is does snow on these days is $.25^9$ and the probability that it does not snow on all other days is $.75^{19}$.
A: But in reality this answer is not accurate because snow on each day is not independent of other days.  For example, it may start snowing at 11:30PM on Feb 1st so that would likely increase the chance that it would snow on Feb 2nd (right after midnight for example).  So the days are NOT independent of each other.
For things like randomly drawn cards and fair coin tosses, calculating probability is meaningful.  For this weather problem, it is only an estimate at best because of the problem stated above, and because past weather is not an assurance of future weather.
