Two gold coins from a mixed bag

Question

A bag contains 3 gold coins and 5 silver coins, 8 in total. You draw one coin and keep it, then draw a second coin. What is the probability that both coins are gold?

Accepted Answer

With only 3 gold coins in the bag, two golds in a row is a long shot. Walk the draws in order. First coin gold. There are 3 gold among 8: \frac{3}{8}. Second coin gold, given the first was gold. Only 2 gold remain among 7 coins: \frac{2}{7}. Multiply for both: \frac{3}{8}	imes\frac{2}{7}=\frac{6}{56}=\frac{3}{28}\approx 0.107. Takeaway. When the wanted color is scarce, drawing two of it without replacement gets hard fast, because taking one out leaves an even thinner supply for the next draw.

Two gold coins from a mixed bag

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