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CAPRINA · Apr 23, 2007, 08:50 AM

In a card deck, what is the probability of drawing a 3 or king from a deck without replacement?

Drawing at least one king when you draw cards from a standard deck 20 times; assume you replace the card each time you draw, so there are always 52 cards to draw from?

please help me break this problem down. Thanks

galactus · Apr 23, 2007, 01:57 PM

Is this two separate problems? Appears to be.

The first one. Consider how many 3's are in a deck? 4

How many kings? 4

Therefore, the proability of drawing a king or 3 is 8/52=2/13.

For the second problem, think binomial probability.

The probability of drawing a king is 1/13.

The opposite of at least 1 is none. So, the probability of getting no kings is 48/52=12/13.

We find the probability of getting no kings and subtract from 1.

$(\frac{12}{13})^{20}=\text{probability of no kings in 20 draws, with replacement$

$1-(\frac{12}{13})^{20}=\text{probability of at least one king in 20 draws with replacement}$

Also, $\sum_{k=1}^{20}C(20,k)(\frac{1}{13})^{k}(\frac{12} {13})^{20-k}$

You should get the same thing.

Petr Kropotkin · Feb 22, 2010, 06:51 AM

What is the probability of drawing two Aces simultaneously from a deck of cards ?

Is it 4/52 *2/50 ?

Unknown008 · Feb 22, 2010, 07:35 AM

No, it's not.

Taking two cards simultaneously is just the same as taking two cards consecutively, without replacement.

Can you post the right answer now?

And next time, please start your own thread.

Pnjovu · Nov 17, 2010, 08:41 AM

Where there are 1388 draws what is the probability of drawing a heart or black card in a deck of 52 cards without replacement