Hey NHQ,

I don't really feel right doing your homework for you, but I don't mind giving you some help.

You're probably studying the Binomial Distribution, right?

In an experiment consisting of n independent trials in which an event has a probability p in a single trial, the probability P(x) of obtaining x successes is:
P(x) = C(n,x)*(p^x)*((1-p)^(n-x))
where C(n,x) = n! / (x!(n-x)!)

Hopefully this isn't greek to you. The calculations are straight forward but can be tedious (especially for parts (c) and (d)).

To find p for each event, take the number of appropriate color slots and divide by the total number of slots. For example, if you were looking at the chance of landing in a Christmas color (red or green), you'd calculate that p = (18 red) + (2 green) / (38 total) = 20/38.

To make the calculations less complicated, you can often figure out chance of the opposite of what you want, and subtract that result from 100%. For example, imagine you're going to get either $0, $10, or $20 for Christmas. If I told you that there was a 30% of getting $0 and a 20% of getting $10, then you'd be able to figure out that you have a 100%-30%-20% = 50% chance of getting $20.


a) To find P(x>=2), you'd normally have to add P(2) + P(3) + P(4) + .... + P(24) + P(25). That's a lot of adding. You can use the subtration trick to reduce the calculation you need to do: P(x>=2) = 1 - P(x<2) = 1 - P(0) - P(1).

b) Haven't we already done this?

c) Yuck. I don't think we can cut any corners here. Just calculate P(x>=15) = P(15) + P(16) + ... + P(14) + P(25). I don't suppose your teacher gave you a table of all of the P(x) values?

d) Ditto. P(x<=10) = P(0) + P(1) + ... + P(9) + P(10)


Hope this helped some,
PP