Two black stones from a bowl

Question

A bowl contains 7 black stones and 2 white stones, 9 in total. You lift out one stone, keep it, then lift out a second stone. What is the probability that both stones are black?

Accepted Answer

Since the first stone stays out, the bowl is different for the second lift. Handle the draws in sequence. First stone black. There are 7 black among 9: \frac{7}{9}. Second stone black, given the first was black. Now 6 black remain among 8 stones: \frac{6}{8}=\frac{3}{4}. Both must be black, so multiply: \frac{7}{9}	imes\frac{3}{4}=\frac{21}{36}=\frac{7}{12}\approx 0.583. Because black stones dominate the bowl, the chance is above one-half. Takeaway. When one color heavily outnumbers the other, back-to-back draws of that color stay likely, but each draw still nudges the odds down a little as …

Two black stones from a bowl

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