Topic: Engineering Mathematics
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
Answer: D. 41/70
Explanation: The probability of randomly choosing either purse is 1/2. The probability of getting a copper coin from the first purse (which has 4 copper out of 7 total coins) is 4/7. The probability of getting a copper coin from the second purse (which has 6 copper out of 10 total coins) is 6/10. The total probability of drawing a copper coin is the sum of the probabilities of choosing each purse and then drawing a copper coin from it: P = (1/2 * 4/7) + (1/2 * 6/10) = 2/7 + 3/10 = (20 + 21) / 70 = 41/70.