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Home  >>  CBSE XII  >>  Math  >>  Probability
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There are two bags,one of which contains 3 black and 4 white balls while the other contains 4 black and 3 white balls.A die is thrown.If it shows up 1 or 3,a ball is taken from the 1st bag,but it shows up any other number,a ball is chosen from the second bag.Find the probability of choosing a black ball.

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  • \(E_1=1 \;Bag\; is\; chosen\)
  • \(E_2=2 \;Bag\; is\; chosen\)
  • \(A\;choising\;a\;black\;ball\)
  • \(P(A)=P(E_1)P(A/E_1)+P(E_2)P(A/E_2)\)
  • \(bag\; 1\; is\; chosen\; if \;1 \;or\; 3\; appear \;in \;throw\; of\; die\)
  • \(P(E_1)=\Large\frac{2}{6}=\frac{1}{3}\)
  • \(bag\; 2\; is\; chosen\; otherwise\)
  • \(P(E_1)=1-\Large\frac{1}{3}=\frac{2}{3}\)
\(P(A/E_1\))=\(P(getting\;black\;ball\;/1\;bag\;is\;chosen)\)
=\(\Large\frac{3}{7}\)
\(P(A/E_2\))=\(P(getting\;black\;ball\;/1\;bag\;is\;chosen)\)
=\(\Large\frac{4}{7}\)
\(P(A)=P(getting\;black\;ball\))
=\(\Large\frac{1}{3}\)\(\times\)\(\frac{3}{7}\)+\(\frac{2}{3}\)\(\times\)\(\frac{4}{7}\)
=\(\Large\frac{11}{21}\)
answered Mar 2, 2013 by poojasapani_1
edited Apr 9, 2014 by pady_1
 

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