# Math Help - [SOLVED] Drawing cards

1. ## [SOLVED] Drawing cards

If three men draw a card from a deck and it's replaced before the next person draws? What are the chances of each drawing the same card?
I thought

$1/52 * 1/52 * 1/52$

would do the trick, but that doesn't give the answer in the book which is 0.00037

thanks.

2. ## I think I understand why now...

Well I worked out that this formula results in the answer at the end of the book.
$52 * 1/52 * 1/52 * 1/52$

I'm still trying to understand why, but I think it's becuase there are 52 single cards in the deck, just like if I was to roll two dice and get a 9, there are four ways out of the thirty-six simple events that can result in a 9. So I'm thinking that you have to multiply it by 52 because there are 52 different simple events that could be the single card chosen by the first person.

regards.

3. Originally Posted by Bucephalus
Well I worked out that this formula results in the answer at the end of the book.
$52 * 1/52 * 1/52 * 1/52$

I'm still trying to understand why, but I think it's becuase there are 52 single cards in the deck, just like if I was to roll two dice and get a 9, there are four ways out of the thirty-six simple events that can result in a 9. So I'm thinking that you have to multiply it by 52 because there are 52 different simple events that could be the single card chosen by the first person.

regards.
You are on the right track. Try thinking about it this way.

The first person draws a card. Then the second person draws a card. Regardless of the first card, the probability that the second card matches it is 1/52. So when the third card is drawn...

See if you can finish.