Two red marbles in a row

Question

A cloth bag holds 5 red marbles and 3 green marbles, 8 in total. Without looking, you pull out one marble, keep it in your hand, then pull out a second marble.

What is the probability that both marbles you pulled are red?

Accepted Answer

The key idea is that once you take a marble out, it is gone: the bag shrinks, so the two draws are not independent. We handle this by walking through the draws in order and multiplying the chances. First marble is red. The bag starts with 5 red out of 8 total, so the chance the first is red is \frac{5}{8}. Second marble is red, given the first was red. After removing one red, only 4 reds remain and the bag now has 7 marbles, so the chance is \frac{4}{7}. Multiply the two stages together, because we need the first and the second to be red: \frac{5}{8}	imes\frac{4}{7}=\frac{20}{56}=\frac{5}{14…

Two red marbles in a row

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