JEE Advanced 2022 Paper 1 · Mathematics · Probability · easy

Urn A contains 3 red and 2 blue balls; urn B contains 2 red and 4 blue balls. if the number is 1 or 2 urn A is chosen, otherwise urn B. Two balls are…

Numerical answer

Urn

A

contains 3 red and 2 blue balls; urn

B

contains 2 red and 4 blue balls. A fair die is thrown: if the number is 1 or 2 urn

A

is chosen, otherwise urn

B

. Two balls are then drawn without replacement from the chosen urn. Given that the two balls drawn are of different colours, find the probability that urn

A

was chosen. Give the answer correct to two decimal places.

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Answer: 0.36

Use Bayes' theorem.

P(A)=\frac13,\ P(B)=\frac23

. For urn

A

P(\text{different})=\frac{3\cdot2}{\binom52}=\frac{6}{10}=\frac35

. For urn

B

P(\text{different})=\frac{2\cdot4}{\binom62}=\frac{8}{15}

. Then

P(A\cap D)=\frac13\cdot\frac35=\frac15

and

P(B\cap D)=\frac23\cdot\frac8{15}=\frac{16}{45}

. Hence

P(A\mid D)=\dfrac{1/5}{1/5+16/45}=\dfrac{9/45}{25/45}=\dfrac{9}{25}=0.36

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