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प्रश्न
A purse contains 2 silver and 4 copper coins. A second purse contains 4 silver and 3 copper coins. If a coin is pulled at random from one of the two purses, what is the probability that it is a silver coin?
उत्तर
A silver coin can be drawn in two mutually exclusive ways:
(I) Selecting purse I and then drawing a silver coin from it
(II) Selecting purse II and then drawing a silver coin from it
Let E1, E2 and A be the events as defined below:
E1 = Selecting purse I
E2 = Selecting purse II
A = Drawing a silver coin
It is given that one of the purses is selected randomly
\[\therefore P\left( E_1 \right) = \frac{1}{2} \]
\[ P\left( E_2 \right) = \frac{1}{2}\]
\[\text{ Now } , \]
\[P\left( A/ E_1 \right) = \frac{2}{6} = \frac{1}{3}\]
\[P\left( A/ E_2 \right) = \frac{4}{7}\]
\[\text{ Using the law of total probability, we get} \]
\[\text{ Required probability } = P\left( A \right) = P\left( E_1 \right)P\left( A/ E_1 \right) + P\left( E_2 \right)P\left( A/ E_2 \right)\]
\[ = \frac{1}{2} \times \frac{1}{3} + \frac{1}{2} \times \frac{4}{7}\]
\[ = \frac{1}{6} + \frac{2}{7}\]
\[ = \frac{7 + 12}{42} = \frac{19}{42}\]
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