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klusterfunk · Oct 20, 2011, 10:02 AM

Hey all..

I've had a good handle on probability for a while, but it's a little rusty due to half a decade of disuse.

Help start my gears, if you will. Thanks!
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The probability of drawing a red card from a deck of normal playing cards is 0.5
A magician draws 12 cards from the deck. What is the probability that the magician draws 10 red cards?

ebaines · Oct 20, 2011, 10:17 AM

I will assume that the 12 cards are drawn one after the other without replacement. One way to approach this is to find the probability of drawing 10 reds in a row followed by 2 blacks, and then multiply that by the number of ways that you can arrange 10 reds out of 12 cards.

The probability of drawing 10 reds followed by 2 blacks is:

$<br /> \frac {26}{52} \times \frac {25} {51} \times \frac {24}{50} \times ... \times \frac {17}{43} \times \frac {26} {42} \times \frac {25} {41}\\<br /> = \frac { P(26,10) \times P(26,2)}{P(52,12)}<br />$

Multiply this probability by the number of ways these 12 cards can be arranged, which is C(12,10) = C(12,2) = (12 x 11)/(2x1) = 66.

klusterfunk · Oct 21, 2011, 06:10 AM

Thanks for your help, guys. I got those answers right, and recalled useful concepts.

Much obliged!

biggkali · Sep 2, 2012, 12:23 PM

you have a standard deck of 52 cards, with ace to king in all four suits, what is the probability of drawing a 9 of any suit?

ebaines · Sep 3, 2012, 08:08 AM

You can find the probability of drawing a particular type of card by dividing the number of cards that satisfy the condition by the number of cards in the deck. For example. The probability of drawing a card of the spade suite is found by dividing the number of spades (13) by the number of cards (52) to get 13/52 = 1/4. So for this problem ask yourself: how many 9's are there in a deck, and divide that by the number of cards in the deck. What do you get for an answer?