# Counting Techniques.

• Oct 24th 2009, 01:48 PM
jebckr
Counting Techniques.
An exam consists of 10 multiple choice questions (each question with 3 choices). If a student guesses at every answer, what is the pobability that he/she will get 6 questions correct?

Is the correct answer C(10,6)/3^10? Or .36%?

Please let me know if I'm making a mistake here.
• Oct 24th 2009, 01:57 PM
mr fantastic
Quote:

Originally Posted by jebckr
An exam consists of 10 multiple choice questions (each question with 3 choices). If a student guesses at every answer, what is the pobability that he/she will get 6 questions correct?

Is the correct answer C(10,6)/3^10? Or .36%?

Please let me know if I'm making a mistake here.

X ~ Binomial(n = 10, p = 1/3).

$\displaystyle \Pr(X = 6) = ^{10}C_6 \left( \frac{1}{3} \right)^6 \left( 1 - \frac{1}{3} \right)^{10 - 6}$.
• Oct 24th 2009, 02:04 PM
jebckr
So it's 5.66%?
• Oct 24th 2009, 03:14 PM
mr fantastic
Quote:

Originally Posted by jebckr
So it's 5.66%?

Well, if you have pressed the correct buttons on your calculator then I suppose this would be the correct answer (expressed as a percentage. Personally, expressing probabilities such as this as a percentage is something I do not like. But that's just me).