Binomial formula: Here is a good math question but there is several parts?

Question

I am learning the binomial formula today and I want to see if I am getting it...

A 10 question multiple choice exam is given, and each question has five possible answers. I take the exam and guess at every question. Using the binomial formula, how could I find the probablility (to 5 decimal places) that:
a) I get exactly 2 questions right
b) I get no q's right
c) Get at least 1 question right
d) I get exactly 2 right (w/out using the binomial formula)

Answer 1

So, why don't you try to answer the questions yourself and show your work. Then we can tell you whether you've got the right idea.

Answer 2

Kevin, if you want 5 decimal places, hire a tutor. Here, WYSIWYG (free advice means you cant be choosy).

OK, the probability of success on each trial is 0.2, aand since you either get the answer right or you get it wrong, the probability of failure is 0.8. The distrubution for a ten answer quiz is (0.2+0.8)^10.
Each term gives you the probabilty of an exact outcome. Since we are at the low end of the result, we want to look at the last terms. They are:
A=Exactly none correct= (0.8)^10
B=Exactlfy one correct = 10 (0.2) (0.8)^9
C=Exactly two correct = (10x9/1x2) (0.2)^2 (0.8)^8
Evaluate C to answer a.
Evaluate A to answer b.
Since "at least 1 right" means that any outcome except A, the probability of this is 1-A