Question

To win a lottery, 6 numbers are drawn at random from a pool of 50 numbers. Numbers cannot repeat. You have one lottery ticket. What is the probability you hold the winning ticket?

Answer 1

(1/50c6). If you have a scientific calculator there is probably a C button on it that stands for combinations. 50C6 will give us the number of ways you can pick 6 items out of a bunch of 50 where order doesn't matter. And putting that over 1 gives us the probability :).

Answer 2

im not sure which one i need to use permutation or combination they confuse me

Answer 3

Permutations are for when order matter and combinations are when it doesn't matter :). " http://www.mathsisfun.com/combinatorics/combinations-permutations.html " is a great site for teaching it.

With combinations it like I said earlier doesn't matter. So if I was counting the number of blue balls I pick out of a bag containing red and blue balls, it wouldn't matter the order of the balls I pick just the number.

With permutations order DOES matter. So like a safe code, it does matter what order you put your code in. I can't describe it too well but that site will be able to :).

Answer 4

so with this one i would use permutation?

Answer 5

Combinations :), does it matter if the 5 ball comes before the 6? All that matters in the case of a lottery is that the 6 numbers chosen appear on your card..

Answer 6

oh ok this is all so confusing right now

Answer 7

\[\frac{ 50! }{ 44!(6! }\]
\[\frac{ 50*49*48*47*46*45 }{ 6*5*4*3*2*1}\]

Answer 8

\[\frac{ 11441304000 }{ 720 }\]
=\[1589070\]

your chance of wining is \[\frac{ 1 }{ 15890700 }\]

Answer 9

^^ i left off a zero

Answer 10

1589070 supposed to be 15890700

Answer 11

That's the answer I got :)

If you can work it out without combinations and permutations that's great

Answer 12

But if the exam board asks specifically for one or the other it might prove a bit of a hard time, so I'de give it one last try to wrap your head round Combs and perms and if that fails then just keep doing it like you just did :)!

Answer 13

yea imma work on the whole figuring out which one i need to use

Answer 14

u have 1 lottery ticket,
there are a total of 50 numbers

Answer 15

and 6 numbers are drawn at random

Answer 16

doesnt 1/15890700 look very less ?

Answer 17

what do you mean

Answer 18

ur chances should be way higher than that tiny number

Answer 19

if u draw the number oly one time itself, the chances of winning are 1/50

Answer 20

when u draw it 6 times, ur chances should go high

Answer 21

They do say you are more likely to be hit by lightning then winning the next lottery :)

Answer 22

Gane but you have to get all 6 correct, you are no longer looking for 1 correct number but 6 making your odds lower

Answer 23

that kinda just almost confused me

Answer 24

Think about it like this, if you have to only guess 1 number from a list of 1-50 the odds are simply 1/50, but now you have to guess 6 numbers correctly, you have guessed the first one correctly but now there another 5 to get correct. Making it a much harder task and therefore having a much lower probability

Answer 25

that makes sense

Answer 26

And then when you have to start thinking about all the different ways these 6 correct answers and 42 incorrect answers are aranged do the really small odds start making sense

Answer 27

this doesnt make sense to me yet, but ok :)

Answer 28

im seeing it as "6 winning tickets in a pool of 50 tickets"
you have one ticket wid u - so the chances should be high.

i do see ur way of interpretation is different. but i find it hard to interpret in any other way... so.. :)

Answer 29

Ah, I see it as 1 ticket yet you have to get 6 correct answers on it instead of 6 tickets all with 1 correct answer on.

Answer 30

Mine is harder to initalliy visualise but it is how real lotteries work so that's why I did it based on that

Answer 31

Also question states "you have one ticket"

Answer 32

xD

Answer 33

uhmm it says "numbers" not "digits"

that part is throwing me off

Answer 34

A lottery ticket has one number, right ?

Answer 35

I have one ticket,
but the lottery company is giving prizes to 6 random tickets... so its okay i guess. for the record - i dint do phd in lottery companies ;p

Answer 36

http://1.bp.blogspot.com/-YTzJOXQv1cE/UEphfhImnKI/AAAAAAAAEOI/CNFrRuC6IVc/s320/LottoCard.jpg - Have a look at that lottery card, you are given 50 numbers and have to cross out 6. If those 6 balls come up in the show you win.

Answer 37

wth was that lol

Answer 38

English national lottery ticket

Answer 39

looks u have more understanding on this topic :)

Answer 40

il go wid u xD

Answer 41

Got my test on this subject next wednesday xD

Answer 42

u wil do super good im sure, i can see :)

Answer 43

Thanks :D.