# 61 cards in a deck. 22 are red, 39 are blue. Whats the % of picking a red card?

• December 24th 2007, 03:49 AM
electricquestion
61 cards in a deck. 22 are red, 39 are blue. Whats the % of picking a red card?
I have 61 cards in my deck. 22 are red, 39 are blue. Whats the percentage of picking up a red card?

Another question to add to that. Lets say this was a game of cards, I have a starting hand of 7 cards, what's the percentage of getting red cards in my starting hand?

Knowing the percentage of having X red cards in my hand, whats the percentage of getting a red card each time I draw afterwards?
• December 24th 2007, 04:20 AM
colby2152
Quote:

Originally Posted by electricquestion
I have 61 cards in my deck. 22 are red, 39 are blue. Whats the percentage of picking up a red card?

Another question to add to that. Lets say this was a game of cards, I have a starting hand of 7 cards, what's the percentage of getting red cards in my starting hand?

Knowing the percentage of having X red cards in my hand, whats the percentage of getting a red card each time I draw afterwards?

$P(red) = \frac{22}{61}$

Percentage of getting red cards in hand means at least one red card in hand?

$P(R > 0) = 1 - P(R \le 0)$
$P(R \le 0) = P(R = 0)$
$P(R = 0) = \frac{39^7}{61*60*59*58*57*56*55}$

I am not sure I understand your last question.
• December 24th 2007, 06:17 AM
electricquestion
Quote:

Originally Posted by colby2152
$P(red) = \frac{22}{61}$

Percentage of getting red cards in hand means at least one red card in hand?

$P(R > 0) = 1 - P(R \le 0)$
$P(R \le 0) = P(R = 0)$
$P(R = 0) = \frac{39^7}{61*60*59*58*57*56*55}$

I am not sure I understand your last question.

I'm doing an experiment, and I'm trying to figure out the percentage of getting a red card in my hand the first turn, as well as the chances of getting a red card each additional draw after it.

The last question I'm trying to figure out from the first card to the last card what my chances of drawing a red card is and whether it decreases or increases in percentages. I'm trying to map out the probability of getting a red card later in the game. In this case, having a red card is a bad thing.

I hope this clears things up. If not I don't know what really to say but, its a card game and I'm trying to find out what odds I have in full.
• December 24th 2007, 07:19 AM
Soroban
Hello, electricquestion!

We're still unclear on the intent of your question.

What is the object of the game?
. . To get a red card on the first draw?
. . To get seven red cards (when dealt seven cards)?
. . To get a red card ... at any time?

$P(\text{Red on 1st draw} \:=\:\frac{22}{62}$

$P(\text{first Red on 2nd draw}) \:=\:\frac{39}{61}\cdot\frac{22}{60}$

$P(\text{first Red on 3rd draw}) \:=\:\frac{39}{61}\cdot\frac{38}{60}\cdot\frac{22} {59}$

$P(\text{first Red on 4th draw}) \:=\:\frac{39}{61}\cdot\frac{38}{60}\cdot\frac{37} {59}\cdot\frac{22}{58}$

. . . and so on . . .