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

Suppose you have two coins which appear identical in your pocket.you know that one is fair and one is 2 headed.If you take one out,toss it and get a head,what is the probability that it was a fair coin?

$\begin{array}{1 1} \frac{1}{3} \\ \frac{2}{3} \\ \frac{1}{2} \\ \frac{3}{4} \end{array} $

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A)
Toolbox:
  • Let us define E\(_1\) Taking a fair coin for toss
  • E\(_2\) Taking a baised coinfor toss
  • P(taking a fair coin for toss/getting a head)
  • P(E\(_1\)/A)\(\Large\frac{{p(E_1)}{P(A/E_1)}}{{P(E_1)}{P(A/E_1)}+{P(E_2)}{P(A/E_2)}}\)
since taking any coin for toss in equally likely
P(\(E_1\))=p(\(E_2\))=\(\large\frac{1}{2}\)
P(A/\(E_1\))=P(getting head when fair coins is taken)
=\(\large\frac{1}{2}\)
P(A/\(E_2\))=P(getting a head when baiased coin is taken)
=\(1\)
=\(\Large\frac{\frac{1}{2}\times\frac{1}{2}}{\frac{1}{2}\times\frac{1}{2}+\frac{1}{2}\times1}\)
=\(\Large\frac{\frac{1}{4}}{\frac{1}{4}+\frac{1}{2}}\)
=\(\Large\frac{1}{4}\times\)\(\frac{4}{3}\)=\(\frac{1}{3}\)

 

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