# Tiles

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• Jul 30th 2010, 12:51 PM
Destroyer0203
Tiles
Somone Please Help. Hypothetically there are 25 tiles. Out of all the tiles 2 have gold coins on them and all the rest are blank. What are the chances that if you draw 5 tiles consecutively without replacement at least one of them will be a gold coin. I used to be able to solve this problem but now i am stuck. At first i thought that you would do 2/25*2/24*2/23*2/22*2/21 but that is the chances of all draws being gold coins with puting back so i was far off. someone help me with a DETAILED explanation.
• Jul 30th 2010, 01:00 PM
Archie Meade
Quote:

Originally Posted by Destroyer0203
Somone Please Help. Hypothetically there are 25 tiles. Out of all the tiles 2 have gold coins on them and all the rest are blank. What are the chances that if you draw 5 tiles consecutively without replacement at least one of them will be a gold coin. I used to be able to solve this problem but now i am stuck. At first i thought that you would do 2/25*2/24*2/23*2/22*2/21 but that is the chances of all draws being gold coins with puting back so i was far off. someone help me with a DETAILED explanation.

Since you say "at least one", then that can be 1 or 2.
Therefore, you may calculate the probability of neither of the 2 gold coins being on the tiles.
Then use the fact that all probabilities sum to 1.

The only possibilities are

(1) no coins
(2) 1 coin (either one)
(2) 2 coins.

Your required probability is (1) or (2) for which we'd sum the probabilities.
You could calculate those.
However, instead you can calculate the probability of (1) and subtract the answer from 1.

Hence, begin with the probability of the first tile not containing a coin is 23/25, the 2nd not containing a coin is 22/24 etc.
• Jul 30th 2010, 01:13 PM
Plato
Quote:

Originally Posted by Destroyer0203
Somone Please Help. Hypothetically there are 25 tiles. Out of all the tiles 2 have gold coins on them and all the rest are blank. What are the chances that if you draw 5 tiles consecutively without replacement at least one of them will be a gold coin.

The probability that neither coin is chosen is $\displaystyle \displaystyle{\frac{\binom{23}{5}}{\binom{25}{5}}}$.

Now ‘at least one’ is the opposite of none. So what is the answer?
• Jul 30th 2010, 01:13 PM
Destroyer0203
first of all thank you for responding so fast, in a matter of minutes in fact. so i tried 23/25* all the way to 19/21 and i ended with around 63%. Can you check my math to make sure? thanks
• Jul 30th 2010, 01:24 PM
Archie Meade
Quote:

Originally Posted by Destroyer0203
first of all thank you for responding so fast, in a matter of minutes in fact. so i tried 23/25* all the way to 19/21 and i ended with around 63%. Can you check my math to make sure? thanks

Yes, that is the percentage chance that no coin will be on any of the tiles.
Hence what is the chance of at least 1 coin being on a tile?
• Jul 30th 2010, 01:32 PM
Destroyer0203
Oh i get it now! out of the the three options it is easier to solve for one instead of 2 so you do 23/25 and reverse it instead of 2/25. So the answer is 37%! thank you very much and for letting me solve it instead of just giving me the answer with no explanation. also thanks for being so prompt in your responses