Q18. The probability that a student knows the correct answer to a multiple choice question is 2/3. If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is 1/4.Given that the student has answered the question correctly, the conditional probability that the student knows the correct answer is*2/33/45/68/9
Question
Q18. The probability that a student knows the correct answer to a multiple choice question is 2/3. If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is 1/4.Given that the student has answered the question correctly, the conditional probability that the student knows the correct answer is*2/33/45/68/9
Solution
To solve this problem, we can use Bayes' theorem, which is a way of finding a probability when we know certain other probabilities. The formula is:
P(A|B) = P(B|A) * P(A) / P(B)
Where:
- P(A|B) is the probability we are trying to find: the student knows the answer given that they answered correctly.
- P(B|A) is the probability that the student answers correctly given that they know the answer, which is 2/3.
- P(A) is the probability that the student knows the answer, which is also 2/3.
- P(B) is the total probability that the student answers correctly, which we can find by adding the probability that they know the answer and answer correctly (2/3 * 2/3 = 4/9) and the probability that they don't know the answer and guess correctly (1/3 * 1/4 = 1/12). So, P(B) = 4/9 + 1/12 = 1/2.
Substituting these values into the formula gives us:
P(A|B) = (2/3 * 2/3) / (1/2) = 8/9
So, the conditional probability that the student knows the correct answer given that they answered correctly is 8/9.
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