so three cards are drawn from a deck of 52 cards. what are the ODDS that all three cards are spades?
how do you do odds? opposed to probability?

- anonymous

- chestercat

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- anonymous

i know that it's the ratio successes :failures
so i tried 13 C3 : 39C3 but it didnt get me the right answer

- cwrw238

the probability that all 3 cards are spades is the product of the individual probabilities

- cwrw238

there are 13 spades in a pack of 52 so
P(3 spades) = 1/4 * 12/51 * 11/50

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## More answers

- anonymous

how about the odds?

- cwrw238

this equals 11/850 as a fraction

- cwrw238

not sure about the odds
I guess its 839 to 11 against it happening
(839 because its 850 - 11)

- anonymous

that's right 11:830

- anonymous

11:839*

- anonymous

but im a bit confused on how to get it

- cwrw238

what part are you confused about?

- anonymous

finding the odds of something

- cwrw238

I dont back horses so I'm not much help there lol

- cwrw238

when you said right 11:839 - was that the answer given in the book or on-line?

- anonymous

answer key from my teacher

- cwrw238

right
well if my memory serves me right there are 2 kins of odds
odds on and odds against
so ithink
11:839 is the odds ON 3 spades being drawn ad
839:11 is the odds AGAINST 3 spades being drawn

- cwrw238

a simple example would be
if a horse has the probability of winning a race
the odds ON will be 1:3
and odds against will be 3:1 - the 2 numbers must add up to 4

- cwrw238

* has the probability 1/4 of winning a race

- anonymous

but for cards, you have to draw 3 cards? so wont that change

- cwrw238

no the rule is still the same
you first work out the probabiility as a fraction
and work out the odds on by subtraction ( in our case 850-11)
your teacher wanted the odds ON drawing 3 spades.

- anonymous

i tried that for another problem. which is now 5 cards are draw... odds of get 5 face cards.

- anonymous

so if i treat it like probability it would be 792/2598960

- cwrw238

some fraction
i have a graphical calculator so i can get that in its most simple form
- its 33/ 108290
- so can you work out the odds from this result?

- anonymous

how did you get that?

- cwrw238

as i said my calculator does the addition of fractions

- anonymous

i mean like the probability in general?

- cwrw238

you could do it manually by finding prime factors but its a bit tedious

- anonymous

how do you know what fractions to add though

- cwrw238

well how did you get your fraction 792/2598960?

- anonymous

the number of successes is 12C5 over total number of outcomes is 52C5

- cwrw238

oh ok thats another way of doing it
the other way
is 12/52 * 11/51 * 10/50 *9/49 * 8/48

- cwrw238

- beceuse theres 12 face cards out of 52 - then we have 11 left out of 51 etc
they are independent evants so the probabilities are multipl;ied

- anonymous

hm, i get a different answer

- cwrw238

you can simplify some of the fractions first
so its same as
3/13 * 11/51 * 1/5 * 9/49 * 1/6

- anonymous

oh i got the answer. thank you xD

- cwrw238

yw

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