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Questions  >>  CBSE XII  >>  Math  >>  Probability
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Q)

Bag I contains 3 black and 2 white balls,Bag II contains 2 black and 4 white balls.A bag and a ball is selected at random .Determine the probability of selecting a black ball.

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A)
Toolbox:
  • Bag 1has 3 Black and 2 White
  • Bag 2has 2 Black and 4 White
  • \(E_1\)=First bag is chosen
  • \(E_2\)=secound bag is chosen
  • A=Black ball drawn
  • P(A)=\(P(E_1\))\(P(A/E_1\))+\(P(E_2\))\(p(B/E_2\))
Probability of choosing Bag 1=Probability of choosing Bag 2
\(P(E_1\))=\(P(E_2\))=\(\large\frac{1}{2}\)
\(P(A/E_1\))=P(getting a black ball if 1 bag is chosen)=\(\large\frac{3}{5}\)
\(p(B/E_2\))=P(getting a black ball if 2bag is chosen)=\(\large\frac{2}{6}\)
P(A)=\(\large\frac{1}{2}\times\)\(\large\frac{3}{5}\)+\(\large\frac{1}{2}\times\)\(\large\frac{2}{6}\)
=\(\large\frac{3}{10}\)+\(\large\frac{1}{6}\)
=\(\large\frac{7}{15}\)

 

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