Posted by **John** on Saturday, January 5, 2013 at 10:27pm.

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 -
**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)

= 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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