2 Probability problems

I am taking statistics at my local community college and am ONLY doing it because it is required for a BSN degree. I am a 4.0 student, but most of my courses have been in science. Math is just not my strong area, so no offense to you who love it.
The first 4 chapters have gone well for me but I have a couple of problems that I am stumped on. This is one of them:

"An unprepared student makes random guesses for the 10 true-false questions on a quiz. Find the probability that he obtained at least one correct answer."

My thoughts were that I should take 1 - 1/1024 = 1023/1024, but that seems really high. Am I headed in the right way?

The second problem is;

"A committee of 11 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the probability that the proposal wins by a vote of 8 to 3?"

I have no idea where to head on this one. The last part is throwing my brain into a tail spin. Could somone please give me clue where to start?

I know this may seem pretty easy for most of you, but again math is NOT my strong area!

Thanks in advance for the help! Heidi


Super Moderator
Thanks in advance for the help! Heidi

Both problems are applications of the Binomial Distribution...

Pr{X} = N!/(X!*(N-X)!) * p^X * q^(N-X) where p is the probability of success and q = 1 - p.

For example, your second question is solved by using for formula above as:

Pr{X=8} = 11!/(8!*3!) * (.5)^8 * (.5)^3 where p=0.5 because voting is random.