Question

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?
1. 70/82
2. 35/70
3. 41/82
4. 41/70

Answer 1

Correct Answer - Option 4 : 41/70

Concept:

1^st purse contains 4 copper and 3 silver coins, so the probability of selecting 1 copper coin from it,

Thus, P (copper coin from 1^st purse) = \(\frac{^4C_1}{^7C_1}\) = \(\frac{4}{7}\) 

2^nd purse contains 6 copper and 4 silver coins, so the probability of selecting 1 copper coin from it,

Thus, P (copper coin from 2^nd purse) = \(\frac{^6C_1}{^10C_1}\)= \(\frac{6}{{10}}\)

And, Probability of selecting any purse = \(\frac{1}{2}\)

Hence, the Probability of selecting a copper coin = \(\frac{1}{2} \times \left( {\frac{4}{7} + \frac{6}{{10}}} \right)\)

Probability of selecting a copper coin = \(\frac{{41}}{{70}}\)