The probability of the drawn ball from U₂ being white is [JEE Adv 2011 P1]

Correct Answer is : 233023/303023

Correct Answer is : 233023/303023

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IIT JEE Advanced 2011 Paper 1

Paragraph for next 2 questions

Let

U_1

and

U_2

be two urns such that

U_1

contains 3 white and 2 red balls, and

U_2

contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from

U_1

and put into

U_2

. However, if tail appears then 2 balls are drawn at random from

U_1

and put into

U_2

. Now 1 ball is drawn at random from

U_2

Section: Mathematics

Question : 58 of 69

Marks: +1, -0

U_2

Solution:

H → One ball from

U_1

U_2

T → Two balls from

U_1

U_2

E: One ball drawn from

U_2

P/W from

U_2

\frac{1}{2}\times\left(\frac{3}{5}\times 1\right) + \frac{1}{2}\times\left(\frac{2}{5}\times\frac{1}{2}\right) + \frac{1}{2}\times\left(\frac{{}^{3}C_{2}}{{}^{5}C_{2}} \times 1\right)

\frac{1}{2}\times\left(\frac{{}^{2}C_{2}}{{}^{5}C_{2}}\times\frac{1}{3}\right) + \frac{1}{2}\times\left(\frac{{}^{3}C_{1} \cdot {}^{2}C_{1}}{{}^{5}C_{2}} \times \frac{2}{3}\right)

\frac{23}{30}

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