SOLUTION: A multiple choice exam consists of 12 questions, each having 5 possible answers. To pass you must answer at least 8 out of 12 correctly. What are your chances if you go into the ex

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Question 1019322: A multiple choice exam consists of 12 questions, each having 5 possible answers. To pass you must answer at least 8 out of 12 correctly. What are your chances if you go into the exam without knowing a thing and have to resort to pure guessing?
Answer by mathmate(429) About Me  (Show Source):
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Question:
A multiple choice exam consists of 12 questions, each having 5 possible answers. To pass you must answer at least 8 out of 12 correctly. What are your chances if you go into the exam without knowing a thing and have to resort to pure guessing?

Solution:
Binomial distribution comes to the rescue.
Probability of X success out of n trials each with a constant probability of p is given by:
P(X;n;p)=C%28n%2CX%29%2Ap%5EX%2A%281-p%29%5E%28n-X%29
where C(n,X) is number of combinations of X objects chosen from n distinct ones.

Here,
n=12,
p=1/5
cases for passing X>=8.
So
P(X>=8;12;1/5)
=Σ C%2812%2Ci%29%2A%281%2F5%29%5Ei%2A%281-1%2F5%29%5E%2812-i%29 for i=8,9,10,11,12
=0.000519+0.000058+0.0000004+0.000000+0.000000
=0.000581