# If I have nine cards, 3 red, 4 blue, and 2 purple, what is the probability of drawing two of the same card?

May 17, 2018

If your question is under that case "without putting the firct card back", the answer is $\frac{20}{72}$

#### Explanation:

There are three propabilities (getting two reds, getting two blues and getting two purples just after trial):

${P}_{1} = \frac{3}{9} \times \frac{2}{8} = \frac{6}{72}$ (getting two reds)

${P}_{2} = \frac{4}{9} \times \frac{3}{8} = \frac{12}{72}$ (getting two reds)

${P}_{3} = \frac{2}{9} \times \frac{1}{8} = \frac{2}{72}$ (getting two purples).

Total probability is the sum of these

$P = \frac{6 + 12 + 2}{72} = \frac{20}{72}$

This is under the condition of when you pick the first card, you do not put it back to the cards.

Your answer is $\frac{20}{72} = \frac{10}{36} = \frac{5}{18}$