Passing Grade Probability Calculation

What is the probability of passing a 10-question true-false quiz by randomly guessing with at least a 70 percent score?

What is a passing grade for the state written knowledge exam with Aceable?

Answer:

The probability of passing a 10-question true-false quiz by randomly guessing with at least a 70 percent score would involve calculating the cumulative probability of getting a minimum of 7 out of 10 questions correct.

The probability of passing a 10-question true-false quiz by randomly guessing with at least a 70 percent score can be a challenging task. To break it down, let's consider each step involved in the calculation:

Firstly, for a student to pass the quiz with at least a 70 percent score, they need to answer at least 7 out of the 10 questions correctly. Since it's a true-false quiz, each question has two possible answers, making the probability of guessing correctly on any single question 0.5.

To find the exact probability of passing, we would need to calculate the cumulative probability of getting exactly 7, 8, 9, or all 10 questions correct. This involves considering all the possible combinations that would result in a passing grade. Since each outcome is binary and independent, careful consideration must be given to the different ways in which a student can achieve the desired score.

Therefore, the process of calculating the probability of passing a 10-question true-false quiz with at least a 70 percent score requires a thorough analysis of the various possible outcomes and their respective probabilities. This mathematical exercise can help provide clarity on the likelihood of passing the quiz through random guessing.