A multiple choice examination has 4 choices for each question. A student has…
2024
A multiple choice examination has 4 choices for each question. A student has studied enough so that the probability they will know the answer to a question is 0.5, the probability that they will be able to eliminate one choice is 0.25, otherwise all 4 choices seem equally plausible. If they know the answer they will get the question right. If not they have to guess from the 3 or 4 choices.
As a teacher you want the test to measure what the student knows. If the student answers a question correctly, what is the probability that they knew the answer ?
- A.
0.61
- B.
0.67
- C.
0.71
- D.
0.77
Attempted by 23 students.
Show answer & explanation
Correct answer: D
Correct Option
Option D: 0.77
Detailed Solution
To find the probability that the student knew the answer given they answered correctly, apply Bayes' theorem: P(Know | Correct).
Given probabilities:
P(Know) = 0.5
P(Eliminate) = 0.25 (guessing 1/3)
P(All plausible) = 0.25 (guessing 1/4)
Total probability of a correct answer:
Total Correct = 0.5 + (0.25 / 3) + (0.25 / 4)
Conditional probability:
P(Know | Correct) = 0.5 / Total Correct ≈ 0.769, which rounds to 0.77.