JEE Advanced 2019 Paper 1 · Mathematics · Probability · hard

Box I contains 4 white and 2 black balls; Box II contains 2 white and 4 black balls. if the outcome is 1 or 2, two balls are drawn one after the…

Single correct option

Box I contains

4

white and

2

black balls; Box II contains

2

white and

4

black balls. A fair die is thrown: if the outcome is

1

2

, two balls are drawn one after the other without replacement from Box I, otherwise two balls are drawn in the same way from Box II. Given that the first ball drawn is white, the probability that the second ball drawn is also white is

A. $\dfrac25$
B. $\dfrac12$
C. $\dfrac49$
D. $\dfrac{8}{45}$

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Answer: (A) $\dfrac25$

Let

W_1,W_2

be the events that the first and second balls are white. The box is Box I with probability

\frac13

and Box II with probability

\frac23

. For Box I,

P(W_1)=\frac46=\frac23

and

P(W_1W_2)=\frac46\cdot\frac35=\frac25

. For Box II,

P(W_1)=\frac26=\frac13

and

P(W_1W_2)=\frac26\cdot\frac15=\frac1{15}

. Total probabilities:

P(W_1)=\frac13\cdot\frac23+\frac23\cdot\frac13=\frac49

and

P(W_1W_2)=\frac13\cdot\frac25+\frac23\cdot\frac1{15}=\frac{8}{45}

. Therefore

P(W_2\mid W_1)=\dfrac{8/45}{4/9}=\dfrac25

. The value

\frac{8}{45}

is the joint probability, and

\frac49

is just

P(W_1)

; the box must not be assumed fixed.

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Original question written in the JEE Advanced 2019 Paper 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake