Two blue tokens drawn together

Question

A jar contains 6 blue tokens and 4 yellow tokens, 10 in total. You reach in and remove one token, set it aside, then remove a second token. What is the probability that both tokens are blue?

Accepted Answer

Because you keep the first token out, the jar changes between the two grabs. Work through the draws in order and multiply. First token blue. There are 6 blue among 10 tokens: \frac{6}{10}. Second token blue, given the first was blue. One blue is gone, leaving 5 blue among 9 tokens: \frac{5}{9}. We need both to happen, so multiply: \frac{6}{10}	imes\frac{5}{9}=\frac{30}{90}=\frac{1}{3}\approx 0.333. Takeaway. Sampling without replacement means each draw sees a smaller, updated jar. Multiply the chance of the first draw by the chance of the second given the first.

Two blue tokens drawn together

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