Independent and dependent events

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Learn it Independent events: multiply the probabilities. Without replacement the second draw depends on the first: one fewer item in total (and one fewer of the colour drawn). Add the probabilities of different orders.

Example: 3 red and 4 blue; two drawn without replacement. P(both red)?

First red: $\frac{3}{7}$.
Second red: $\frac{2}{6}$ (one red and one marble gone).
$\frac{3}{7} \times \frac{2}{6} = \frac{1}{7}$.

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