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Questions › IIT JAM › IIT JAM 2022 › Q25
2 marks, −0.667Statistics › Probability and Bayes' theorem › Repeated trials: binomial and geometric probabilitiesEasyabout 1 min

IIT JAM 2022 Question 25: Probability and Bayes' theorem

The probability of getting a head in a toss of a biased coin is 23\dfrac{2}{3}32​. The coin is tossed three times independently. The probability of getting heads in the first two tosses and a tail in the final toss is

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Answer and worked solution

Answer: (A)

For independent tosses the probability of the specified ordered outcome (head, head, tail) is the product 23⋅23⋅13=427\dfrac{2}{3}\cdot\dfrac{2}{3}\cdot\dfrac{1}{3} = \dfrac{4}{27}32​⋅32​⋅31​=274​.

The answer is (A). No binomial coefficient is used because the exact sequence is fixed.

The trap: (C) 227\dfrac{2}{27}272​

Option (C) uses 13\dfrac{1}{3}31​ for a head somewhere; here heads are required specifically in the first two tosses, so each carries probability 23\dfrac{2}{3}32​.

Plain-text version

The probability of getting a head in a toss of a biased coin is 2/3. The coin is tossed three times independently. The probability of getting heads in the first two tosses and a tail in the final toss is (A) 4/27 (B) 1/8 (C) 2/27 (D) 23/27

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

What this question tests

This question is on Repeated trials: binomial and geometric probabilities, part of Probability and Bayes' theorem in Statistics.

Probabilities from independent repeated experiments.

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Question from the IIT JAM 2022 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.