Question

A student takes an exam containing 11
11
true or false questions. At least 7
7
correct answers are required to pass. If the student guesses, what is the probability that he will pass? Round your answer to four decimal places.

Answer 1

Using the principle of binomial probability, the probability that the student will pass is atleast 7 correct answers are required is 0.1717

Using the binomial probability relation :

• P(x = x) = nCx * p^x * q^(n-x)
• Probability of success, p = 1/2 = 0.5
• q = 1 - p = 1 - 0.5 = 0.5

P(x ≥ 7) = p(x = 7) + p(x = 8) + p(x = 9) + p(x = 10)

Using a binomial probability calculator :

P(x ≥ 7) = 0.1172 + 0.0439 + 0.0097 + 0.00097

P(x ≥ 7) = 0.1717

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