2 Probability problems

#1
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
 

Dragan

Super Moderator
#2
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.