Math Is Fun Forum

Hioj

Member

Registered: 2009-10-25

Posts: 16

Probability when choosing cards

The problem is as follows:
"A card is drawn from a deck of cards, the card is noted and thereafter returned to the deck. This experiment is repeated 12 times. Find the probability for the following events:
A: There are exactly 9 court cards"

There are 3 more events but more or less the same as A, so I omitted them. The formulation of the problem is originally also not in english, I've translated it.

This is what I've got so far:

Total court cards per deck: 12 <=> probability of choosing a court card is 12/52.
Thus the probability for choosing a court card 9 times must be (12/52)^9.

I'm unsure about what to do next. Should I multiply it by (40/52)^3 since that's the probability of the 3 remaining picks from the deck?

Thanks for helping!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability when choosing cards

Hi Hioj;

Because of the replacement this is a simple binomial experiment.

I got.

Last edited by bobbym (2009-10-25 08:56:33)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Probability when choosing cards

You've started well, and you're right that you also need to multiply by (40/52)^3, to account for the non-court cards.

That gets you the probability of picking 9 court cards first, and then 3 others.
If you want the probability of 9 court cards in any arrangement, you need to multiply by the amount of combinations there are.

CCCCCCCCCNNN
CCCCCCCCNNCN
CCCCCCCCNCNN
...

There are 12C9 = 220 combinations, so you multiply the probability by that as well.

The final probability is around 0.00019.

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Why did the vector cross the road?
It wanted to be normal.

Hioj

Member

Registered: 2009-10-25

Posts: 16

Re: Probability when choosing cards

Thanks guys!
I knew it was a binomial experiment, I just couldn't see it had to be (12 9)... I was trying with (52 12) but the answer seemed way off. Thanks again!