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A student takes a ten-question true-false quiz and guesses randomly at every answer, so X ~ B(10, 0.5). What is the probability the student passes with at least 70% correct, meaning P(x≥7)?
AAbout 0.1719
BAbout 0.5000
CAbout 0.0010
DAbout 0.8281
Answer & Solution
Correct answer: A. About 0.1719
1. Random guessing on a true-false question gives p = 0.5 for each of the 10 independent questions, so X ~ B(10, 0.5).
2. Passing with at least 70% correct means at least 7 of 10 questions right, so we need P(x≥7).
3. Summing the binomial probabilities for x = 7, 8, 9, and 10 gives P(x≥7) ≈ 0.1719.
4. Option D is the complement, P(x≤6), and option B mistakes the 50% guessing rate for the passing probability itself.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.3 Binomial Distribution_
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