# Probability of gettig Ace in alternate draws from deck of cards.

• Dec 6th 2011, 04:45 AM
sri340
Probability of gettig Ace in alternate draws from deck of cards.
Amarillo slim and jimmy the Greek alternately draw cards from a (face down) deck of ordinary playing cards. Slim draws first, and his first draw is the ace of diamonds. If they continue drawing alternately, what is the probability that slim will also be the one to draw the ace of spades?
• Dec 6th 2011, 07:11 AM
Soroban
Re: probability
Hello, sri340!

I think I have a very simple solution.

Quote:

Amarillo Slim and Jimmy the Greek alternately draw cards from a (face down) deck of
ordinary playing cards. .Slim draws first, and his first draw is the Ace of Diamonds.
If they continue drawing alternately, what is the probability that Slim will also be the one
to draw the Ace of Spades?

The deck is ordered like this:

. . $\displaystyle \begin{array}{ccccccccccc} A\diamondsuit & \_\_ & \_\_ & \_\_ & \_\_ & \_\!\_ & \hdots & \_\_ & \_\_ \\ ^1 & ^2 & ^{\color{red}3} &^4 & ^{\color{red}5} & ^6 && {\color{red}^{51}} & ^{52} \end{array}$

The $\displaystyle A\spadesuit$ must be at one of the odd-numbered positions.

There are 51 possible positions and 25 odd-numbered positions.

The probability is: .$\displaystyle \frac{25}{51}$