Question

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?

Answer 1

i know that it's the ratio successes :failures

so i tried 13 C3 : 39C3 but it didnt get me the right answer

Answer 2

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

Answer 3

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

Answer 4

how about the odds?

Answer 5

this equals 11/850 as a fraction

Answer 6

not sure about the odds

I guess its 839 to 11 against it happening

(839 because its 850 - 11)

Answer 7

that's right 11:830

Answer 8

11:839*

Answer 9

but im a bit confused on how to get it

Answer 10

what part are you confused about?

Answer 11

finding the odds of something

Answer 12

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

Answer 13

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

Answer 14

answer key from my teacher

Answer 15

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

Answer 16

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

Answer 17

* has the probability 1/4 of winning a race

Answer 18

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

Answer 19

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.

Answer 20

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

Answer 21

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

Answer 22

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?

Answer 23

how did you get that?

Answer 24

as i said my calculator does the addition of fractions

Answer 25

i mean like the probability in general?

Answer 26

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

Answer 27

how do you know what fractions to add though

Answer 28

well how did you get your fraction 792/2598960?

Answer 29

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

Answer 30

oh ok thats another way of doing it

the other way

is 12/52 * 11/51 * 10/50 *9/49 * 8/48

Answer 31

- 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

Answer 32

hm, i get a different answer

Answer 33

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

Answer 34

oh i got the answer. thank you xD

Answer 35

yw