Posted by John on Saturday, January 5, 2013 at 10:27pm.
Mary took a 20 question multiplechoice exam where there are 4 choices for each question and only 1 of those choices is correct. Rather than reading the question, Mary simply puts a random choice of answer down for each question. Determine the probability that Mary gets exactly 8 of the 20 questions correct.

Probability  MathMate, Saturday, January 5, 2013 at 10:56pm
The problem satisfies the following conditions:
the experiment is a Bernoulli experiment (i.e. each trial has one of two outcomes)
 the probability of each trial is known remains constant throughout the experiment
 each trial is independent of the others.
This indicates a binomial distribution.
For exactly 8 correct answers, we calculate as follows:
p=prob. for success (answer correct)
q=prob. for failure (answer incorrect)
= 1p
n=number of trials (20)
r=number of successes (8)
The probability of exactly 8 successes out of 20 is given by
P(8)=C(20,8)p^8q^(208)
where (20,8) is the binomial coefficient for p^8 , where
P(n,r)=n!/(r!(nr)!)
For P(8), I get about 6%, or 0,06
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