Question

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

Answer 1

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

Explanation:

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`