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Questions › IIT JAM › IIT JAM 2024 › Q42
1 markStatistics › Probability and Bayes' theorem › Conditional probability and the multiplication ruleModerateabout 2 min

IIT JAM 2024 Question 42: Probability and Bayes' theorem

Students AAA and BBB solve a problem separately. P(A solves∣B cannot)=15P(A \text{ solves} \mid B \text{ cannot}) = \tfrac{1}{5}P(A solves∣B cannot)=51​, P(B solves∣A solves)=35P(B \text{ solves} \mid A \text{ solves}) = \tfrac{3}{5}P(B solves∣A solves)=53​, and P(A solves)=110P(A \text{ solves}) = \tfrac{1}{10}P(A solves)=101​. Then the probability that BBB can solve the problem is ________ (rounded off to one decimal place).

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Plain-text version

Students A and B solve a problem separately. P(A solves | B cannot) = 1/5, P(B solves | A solves) = 3/5, and P(A solves) = 1/10. Then the probability that B can solve the problem is (rounded off to one decimal place).

Probability and Bayes' theorem has come up 190 times in 7 exams since 2004.

What this question tests

This question is on Conditional probability and the multiplication rule, part of Probability and Bayes' theorem in Statistics.

Probabilities that change when you know something has happened.

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Question from the IIT JAM 2024 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.