Problem 4.     Due 1/31/01

An elementary school class with 100
students has been promised a field
trip to the zoo if 95% of the students
remember to turn in their homework
the week before.  If the probability
of each student -not- to turn in their
homework is 5%, what is the likelihood
that the class will go on the field
trip?

Solve this problem by writing your own
analog to the example program prob.m.
Try to come up with an alternative algorithm
to avoid overflow and underflow errors.

Hint: Develop an algorithm which solves 
for the log of the probability rather than for 
the probability directly.  You might also look
into using the more accurate analog to Stirling's 
formula examined in problem 1 for really large
factorials rather than taking lots of logs.  

Remember that for the class to go on the trip 
either exactly 0, 1, 2, 3, 4, or 5 students would 
have to forget their homework.