Question

In a certain recruitment test, there are multiple-choice questions. there are 4 possible answer to each question, of which one is correct. the probability that a student knows the answer to a question is 90%. if he gets the correct answer to a question. what is the probability that he was guessing?

a. 37/40
b. 1/40
c. 36/40
d. 1/9

Answer 1

The probability that a student was guessing given a correct answer, Bayes' theorem is applied to the information that there is a 90% chance the student knows the answer and a 10% chance they are guessing with four possible answers for each question. The correct answer is option b.

Step-by-step explanation:

The question is asking for the probability that a student was guessing on a question given that they answered it correctly and is based on probability theory. Since the student knows the answer with a 90% chance, there is a 10% chance that they are guessing.


If guessing, the chance of getting the correct answer is 1 out of 4, since there are four possible answers. We use Bayes' theorem to find the probability that they were guessing, given that they answered correctly.

The solution involves the following steps:

1. Calculate the probability of guessing and getting the question right: P(Guess and Correct) = P(Guess) * P(Correct | Guess) = 0.10 * 0.25.
   
   
2. Calculate the probability of knowing the answer and getting the question right: P(Know and Correct) = P(Know) * P(Correct | Know) = 0.90 * 1.
   
   
3. Calculate the total probability of getting the question right: P(Correct) = P(Guess and Correct) + P(Know and Correct).
   
   
4. Use Bayes' theorem to find the probability of guessing given a correct answer: P(Guess | Correct) = P(Guess and Correct) / P(Correct).

The correct answer to the original question is computed to be option b. 1/40 or 0.025 when following these steps, indicating a very low probability that the student was guessing even though they answered correctly.