An exam consists of 12 questions, each having 5 possible answers. To pass, you must answer at least 8 out of 12 questions correctly. What are your chances of passing if you go into the exam without knowing anything and resort to pure guessing?

Question

19-02-2025
Mathematics

High School

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An exam consists of 12 questions, each having 5 possible answers. To pass, you must answer at least 8 out of 12 questions correctly. What are your chances of passing if you go into the exam without knowing anything and resort to pure guessing?

Answer :

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Final answer:

To calculate the chances of passing the exam by pure guessing, we need to calculate the probability of getting at least 8 out of 12 questions correct. We can use the binomial probability formula to determine the individual probabilities of getting 8, 9, 10, 11, or 12 questions correct and add them together.

Explanation:

To calculate the chances of passing the exam by pure guessing, we need to calculate the probability of getting at least 8 out of 12 questions correct. Since each question has 5 possible answers, the probability of guessing the correct answer is 1/5.

To find the probability of getting exactly 8, 9, 10, 11, or 12 questions correct, we can use the binomial probability formula. The formula is:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k),

where n is the number of trials (12), k is the number of successes (8, 9, 10, 11, or 12), p is the probability of success (1/5), and C(n, k) is the number of combinations of n objects taken k at a time.

By calculating the probabilities for getting 8, 9, 10, 11, or 12 questions correct and adding them together, we can find the total probability of passing the exam by pure guessing.