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प्रश्न
A bag contains 3 red and 2 black balls. One ball is drawn from it at random. Its colour is noted and then it is put back in the bag. A second draw is made and the same procedure is repeated. Find the probability of drawing (i) two red balls, (ii) two black balls, (iii) first red and second black ball.
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उत्तर
\[\text{ Given: Bag contains 3 red and 2 black balls } . \]
\[\text{ Let three red balls be } R_1 , R_2 \text{ and } R_3 \text{ and 2 black balls be } B_1 \text{ and } B_2 . \]
\[\text{ Sample space } :\]
\[{\left(R_1 , R_2 \right), \left( R_1 , R_3 \right), \left( R_1 , B_1 \right), \left( R_1 , B_2 \right), \left( R_1 , B_3 \right)}\]
\[\left( R_2 , R_3 \right), \left( R_2 , B_1 \right), \left( R_2 , B_2 \right)\left( R_3 , R_3 \right)\]
\[\left( i \right)P\left( \text{ drawing two red balls } \right) = \frac{9}{25}\]
\[\left( ii \right)P\left( \text{ drawing two black } \right) = \frac{4}{25}\]
\[\left( iii \right)P\left( \text{ first red and second black } \right) = \frac{6}{25}\]
