Statistics

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You have a ten question multiple choice test in your next class and you did not study at all. Each question has four choices and only one correct answer. You are going to guess on each question. What is the probability that you score at least a 20% on the test.

• Statistics -

Use binomial probability because:
probability is known and does not change over the experiment,
outcome is binomial (success or failure),
each step of the experiment is similar,

p=0.25
n=10
P(r)=number of question correct
=nCr(p^r)(1-p)^(n-r)

nCr = binomial coefficient = n!/((n-r)!r!)

P(0)=0.0563 (zero question correct)
P(1)=0.1877 (1 question correct)

Therefore, to get at least 20%, or 2 or more questions correct, we have
P(2+)=1-(P(0)+P(1))
=0.7560

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