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ISRO 2014- Probability [Mech]

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A purse contains 4 copper coins and 3 silver coins. A second purse contains 6 copper coins and 4 silver coins. A purse is chosen randomly and a coin is taken out of it. What is the probability that it is a copper coin?
 

a) 70/82

b) 35/70

c) 41/82

d) 41/70
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P{Copper Coin} = P{Copper Coin taken out from $1$st purse} + P{Copper Coin taken out from $2$nd purse}

P{Copper Coin} = $\frac{1}{2}\left ( \frac{4}{7}\right ) + \frac{1}{2}\left ( \frac{6}{10} \right )$

P{Copper Coin} = $\frac{41}{70}$
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Let, Probability of choosing a copper coin overall= P(C)

Probability of choosing a copper coin From bag A= P(A)

Probability of choosing a copper coin From bag B= P(B)

Probability of choosing a Bag= 1/2

P(C)=1/2 x P(A) + 1/2 x P(B) =  1/2 x 4/7 + 1/2 x 6/10 = 41/70
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