# Probability

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Mary took a 20 question multiple-choice 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 -

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:
= 1-p
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^(20-8)
where (20,8) is the binomial coefficient for p^8 , where
P(n,r)=n!/(r!(n-r)!)
For P(8), I get about 6%, or 0,06

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