In this scenario, there are only 2 possible outcomes. It is either the answer is correct or wrong.Since the outcomes are independent, it means that it is binomial probability. We would apply the binomial distribution formula which is expressed as
P(x) = nCx * p^x * q^(n - x)
where
n is the sample size
x is the number of successes
p is the probability of success
q = 1 - p = probability of failure
From the information given,
p = 1/4 = 0.25
q = 1 - 1/4 = 3/4 = 0.75
n = 12
x = 5
We want to find P(x = 5)
P(x = 5) = 12C5 * 0.25^5 * 0.75^(12 - 5)
P(x = 5) = 0.103
The probability that among 12 test subjects, exactly 5 answers are correct is 0.103
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