Question

A bag contains 4 white and 5 black balls. Another Bag contains 9 white

and 7 black balls. A ball is transferred from first bag to the second and

then a ball is drawn at random from second bag. Find the probability that

ball drawn is white.

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Answer 1

$\huge\pink{\boxed{\blue{\boxed{ \purple{ \boxed{{\pink{Answer}}}}}}}} \\ \large\pink{\boxed{\blue{\boxed{ \purple{ \boxed{{\pink{Your~answer↓}}}}}}}} \\ Two \: cases \: arises \\ </p><p>Case 1. \: When \: transfer \: ball \: from \: bag \: is \: white \: in \: color. \\ </p><p>The \: probability \: of \: getting \: white \: ball \: from \: first \: bag = \frac{4}{9} \\ </p><p>Now, \: white \: ball \: is \: transfer \: to \: Bag 2, \\ now \: getting \: probability \: of white \: ball \: from \: second \: bag \: is \: \frac{10}{17} \\ </p><p>Case 2. When \: transfer \: ball \: from \: bag \: 1\: is \: black \: in \: color. \\ </p><p>The \: probability \: of \: getting \: black \: ball \: from \: first \: bag = \frac{5}{9} \\ </p><p>Now, \: black \: ball \: is \: transfer \: to \: Bag \: 2, \\ now \: getting \: probability \: of \: white \: ball \: from \: second \: bag \: = \frac{9}{17} \\ </p><p>So \: required \: probability = \frac{4}{9} \times \frac{10}{17} + \frac{5}{9} \times \frac{9}{17} \\ = \frac{40 + 45}{17 \times 9} \\ = \frac{85}{17 \times 9} \\ = \frac{5}{9}$