posted by John .
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.
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)
n=number of trials (20)
r=number of successes (8)
The probability of exactly 8 successes out of 20 is given by
where (20,8) is the binomial coefficient for p^8 , where
For P(8), I get about 6%, or 0,06