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

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Answer 1 · 2018-05-17T09:47:59

If your question is under that case "without putting the firct card back", the answer is #20/72#

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

#P_1 = 3/9 times 2/8 = 6/72# (getting two reds)

#P_2 = 4/9 times 3/8 = 12/72# (getting two reds)

#P_3 = 2/9 times 1/8 = 2/72# (getting two purples).

Total probability is the sum of these

#P = (6+12+2)/72 = 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 #20/72 = 10/36 = 5/18#