anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • 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
  • cwrw238
the probability that all 3 cards are spades is the product of the individual probabilities
cwrw238
  • cwrw238
there are 13 spades in a pack of 52 so P(3 spades) = 1/4 * 12/51 * 11/50

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anonymous
  • anonymous
how about the odds?
cwrw238
  • cwrw238
this equals 11/850 as a fraction
cwrw238
  • cwrw238
not sure about the odds I guess its 839 to 11 against it happening (839 because its 850 - 11)
anonymous
  • anonymous
that's right 11:830
anonymous
  • anonymous
11:839*
anonymous
  • anonymous
but im a bit confused on how to get it
cwrw238
  • cwrw238
what part are you confused about?
anonymous
  • anonymous
finding the odds of something
cwrw238
  • cwrw238
I dont back horses so I'm not much help there lol
cwrw238
  • cwrw238
when you said right 11:839 - was that the answer given in the book or on-line?
anonymous
  • anonymous
answer key from my teacher
cwrw238
  • 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
  • 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
  • cwrw238
* has the probability 1/4 of winning a race
anonymous
  • anonymous
but for cards, you have to draw 3 cards? so wont that change
cwrw238
  • 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
  • anonymous
i tried that for another problem. which is now 5 cards are draw... odds of get 5 face cards.
anonymous
  • anonymous
so if i treat it like probability it would be 792/2598960
cwrw238
  • 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
  • anonymous
how did you get that?
cwrw238
  • cwrw238
as i said my calculator does the addition of fractions
anonymous
  • anonymous
i mean like the probability in general?
cwrw238
  • cwrw238
you could do it manually by finding prime factors but its a bit tedious
anonymous
  • anonymous
how do you know what fractions to add though
cwrw238
  • cwrw238
well how did you get your fraction 792/2598960?
anonymous
  • anonymous
the number of successes is 12C5 over total number of outcomes is 52C5
cwrw238
  • cwrw238
oh ok thats another way of doing it the other way is 12/52 * 11/51 * 10/50 *9/49 * 8/48
cwrw238
  • 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
  • anonymous
hm, i get a different answer
cwrw238
  • cwrw238
you can simplify some of the fractions first so its same as 3/13 * 11/51 * 1/5 * 9/49 * 1/6
anonymous
  • anonymous
oh i got the answer. thank you xD
cwrw238
  • cwrw238
yw

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