multiple choice, maths probability question....!

[andyandy]

if there are 36 questions in a multiple choice exam, with 4 possibilities, what is the probability of getting 50% (or eg 75%) by guessing alone?

obviously the prob per guess is 1/4, so you'd expect about 9 right by guesswork....

as a start, it's going to be something like this, no....?

(1/4)^n(3/4)^(36-n) = prob

but then do you have to put in a binomial bit? (36 choose n) or something?

cheers :)

[Professor Yaffle]

Where are our 4 possible answers to choose from?

[andyandy]

Where are our 4 possible answers to choose from?

:D

[Jorghnassen]

Yes, this is binomial, thus
P(X \geq x) = \displaystyle \sum_{k=x}^{36} {36 \choose k} (1/4)^k (3/4)^{36-k} = \frac{1}{4^{36}} \sum_{k=x}^{36} {36 \choose k} 3^{36-k}
For 50%, put x= 18, 75%, use x=27, etc.

Oh yes, if you just want the probability of exactly x, forget the sum part.

[boooeee]

if there are 36 questions in a multiple choice exam, with 4 possibilities, what is the probability of getting 50% (or eg 75%) by guessing alone?

obviously the prob per guess in 1/4, so you'd expect about 9 right by guesswork....

as a start, it's going to be something like this, no....?

(1/4)^n(3/4)^(36-n) = prob

yes

but then do you have to put in a binomial bit? (36 choose n) or something?

yes

This will tell you the probability of getting exactly n. No more, no less.

[drkitten]

if there are 36 questions in a multiple choice exam, with 4 possibilities, what is the probability of getting 50% (or eg 75%) by guessing alone?


In case you wanted the actual answer, the probability of getting exactly 50% is 0.0007
The probability of getting at least 50% is 0.0011
The probability of getting exactly 75% is zero to five significant figures.

[Jeff Corey]

Use one of these and enter p=.25 http://www.graphpad.com/quickcalcs/binomial2.cfm

[andyandy]

great, cheers!

Good to see i was on the right lines :D

[UNLoVedRebel]

edit my latex skills suck.

[Jeff Corey]

"latex"?

[GodMark2]

"latex"?

The math in Jorghnassen's message was written in \LaTeX for the fancy formatting.

[Jeff Corey]

Sorry, I thought it was this. http://www.mccullagh.org/db9/1ds-3/red-latex-folsom-street.jpg