Probability · Class 12 · CBSE · Science Mathematics

The probability that a student has studied for a test is 0.6. The probability of answering a question correctly is 0.8 if the student has studied and…

Practice question from Probability (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-9D3D61

The probability that a student has studied for a test is 0.6. The probability of answering a question correctly is 0.8 if the student has studied and 0.3 if the student has not studied. If the student answers correctly, what is the probability that the student had studied?

  1. A.0.6
  2. B.0.7
  3. C.0.8Correct answer
  4. D.0.9

Solution

By Bayes' theorem, P(S∣C)=P(S)P(C∣S)P(S)P(C∣S)+P(S′)P(C∣S′)=0.6×0.80.6×0.8+0.4×0.3=0.8P(S\mid C)=\frac{P(S)P(C\mid S)}{P(S)P(C\mid S)+P(S')P(C\mid S')}=\frac{0.6\times0.8}{0.6\times0.8+0.4\times0.3}=0.8.

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