Posted by **Danielle** on Friday, December 14, 2007 at 12:44pm.

I do not understand the binomial theorem. One of my questions is "there are 5 mutiple choice questions with 4 possible answers each. What is the probability of getting more than 3, exactly 3, and less than 3 correct?"

Thanks for any help:)

- math-binomial prob -
**drwls**, Friday, December 14, 2007 at 1:18pm
Use the binomial theorem to get the possibility of 0,1,2,3,4 and 5 correct.

For zero correct, the probability is just (3/4)^5 = 0.2373. 3/4 is the probability of getting each one wrong.

For five correct, the probability is

(1/4)^5 = 0.0001

For one correct, (one success and 4 failures) the probability is

5!/[1!*4!]*(1/4)*(3/4)^4

= 5(.25)(.3164) = 0.3955

(That is where you need the binomial theorem)

For two correct, using the same theorem, the probability is

[5!/(3!*2!)](1/4)^2*(3/4)^3

= 10*(0.25)^2(0.4219)= 0.2637

For three correct, the probability is

5!/[2!*3!)](1/4)^3*(3/4)^2 = 0.0879

For four correct, the probability is

(5!/4!)(1/4)^4*(3/4)= 5*.0039*.3164 = 0.0195

Use these results to get the probabilities for >3 and <3 right.

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