Two white beads pulled from a pouch

Question

A pouch holds 4 red beads and 5 white beads, 9 in total. You draw one bead and keep it, then draw a second bead. What is the probability that both beads are white?

Accepted Answer

The pouch shrinks after the first draw, so treat the draws one at a time. First bead white. There are 5 white out of 9: \frac{5}{9}. Second bead white, given the first was white. Now 4 white remain out of 8 total: \frac{4}{8}=\frac{1}{2}. Multiply for both draws: \frac{5}{9}	imes\frac{1}{2}=\frac{5}{18}\approx 0.278. Takeaway. After each draw, recount what is left. The second white draw is easier to picture as "4 of the remaining 8," which reduces neatly to one-half.

Two white beads pulled from a pouch

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