Question:
An unprepared student takes five questions of true-false type quiz and guesses every answer. What is the probability that the student will pass the quiz if at least four correct answers is the passing grade?
An unprepared student takes five questions of true-false type quiz and guesses every answer. What is the probability that the student will pass the quiz if at least four correct answers is the passing grade?
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For true-false type questions, use the binomial distribution to calculate the probability of correct answers based on the number of questions and probability of success.
Updated On: Apr 27, 2026
- \( \frac{1}{16} \)
- \( \frac{3}{16} \)
- \( \frac{1}{32} \)
- \( \frac{3}{32} \)
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The Correct Option is B
Solution and Explanation
Step 1: Binomial distribution application.
The number of correct answers follows a binomial distribution with parameters \( n = 5 \) and \( p = \frac{1}{2} \). We calculate the probability of getting at least 4 correct answers.
Step 2: Conclusion. Thus, the probability that the student will pass the quiz is \( \frac{3}{16} \).
Step 2: Conclusion. Thus, the probability that the student will pass the quiz is \( \frac{3}{16} \).
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