Probability question

inogen · 17 Apr 2013 at 10:54

WillyNelson said:
Indeed. I deal with profitability not probability.

It's a long time since I did a Statistics GCSE and I just wanted to check. I was correct after all.

Jono8 said:
Ha. No wonder our economy is going down the toilet.

KERBLAMMO!!

Jono8 · 17 Apr 2013 at 10:55

WillyNelson said:
It's unlikely.

as is evident.

WillyNelson · 17 Apr 2013 at 11:03

[FnG]magnolia;24132655 said:
Probably.

Certainly.

I deal with events that have already happened.

inogen · 17 Apr 2013 at 12:25

WillyNelson said:
Certainly.

I deal with events that have already happened.

Yeah cos doing the maths on stuff that's happened is different than doing the maths on stuff that hasn't happened yet.

That's obvisouly why I wasn't very good at stats. I never saw the difference.

geuben · 17 Apr 2013 at 12:39

skyripper said:
If there is only one winning ticket drawn, then 1:5 and 5:25 are the same.

If there is more than one winning ticket being drawn, then it is better to have 5:25 rather than 1:5.

Are you sure about that?

Example:

3 tickets are drawn in a raffle, what is the probability that you will have 1 winning ticket if:

a) there are 5 possible tickets and you have 1 ticket
b) there are 25 possible tickets and you have 5 tickets

Answers:

a) Odds of getting 1st winning ticket: 1/5
Odds of getting 2nd winning ticket: 1/4
Odds of getting 3rd winning ticket: 1/3

Total odds: (1/5)+(1/4)+(1/3) = 47/60 = 0.7833r

b) Odds of getting 1st winning ticket: 5/25
Odds of getting 2nd winning ticket: 5/24
Odds of getting 3rd winning ticket: 5/23

Total odds: (5/25)+(5/24)+(5/23) = 1727/2760 = 0.6257

WillyNelson · 17 Apr 2013 at 12:42

inogen said:
Yeah cos doing the maths on stuff that's happened is different than doing the maths on stuff that hasn't happened yet.

When dealing with probablility, which we are, then yes they are different. Insofar as events which have happened are certainties and probability doesn't come into it.

[FnG]magnolia · 17 Apr 2013 at 12:43

I have one sandwich and I cut it in two.

! WHERE DID THE OTHER SANDWICH COME FROM !

danza · 17 Apr 2013 at 12:52

You are handed it when you realise that you have two halves of one sandwich. So now there are two; one in two halves, and one whole sandwich.

mufc802 · 17 Apr 2013 at 12:54

1/5 = 5/25 = 0.2 = 20%

dirtychinchilla · 17 Apr 2013 at 12:56

Did you try dividing 5 by 25, because that equals 1/5.

Jono8 · 17 Apr 2013 at 12:58

[FnG]magnolia;24133271 said:
I have one sandwich and I cut it in two.

! WHERE DID THE OTHER SANDWICH COME FROM !

What other sandwich?

Pneumonic · 17 Apr 2013 at 13:00

assuming that only 1 ticket is drawn in the raffle then the chance is equal.. if you have multiple draws then the chance is not the same to win across all draws.

inogen · 17 Apr 2013 at 13:50

WillyNelson said:
When dealing with probablility, which we are, then yes they are different. Insofar as events which have happened are certainties and probability doesn't come into it.

It's future, present, or past tense, a mixture of all, some or none is irrelevant.

1/5 = 5/25

It's maths. You're confused.

What if I asked you, "I bought 5 raffle tickets yesterday, there were a total of 25 tickets, what was the probability that I won?". Would you be able to solve that?

inogen · 17 Apr 2013 at 14:05

Pneumonic said:
assuming that only 1 ticket is drawn in the raffle then the chance is equal.. if you have multiple draws then the chance is not the same to win across all draws.

Yeah, that's true.

If it's multiple draws then it does complicate matters somewhat. Each draw can be shown as x/y where x is the number of tickets bought minus those that have won and where y is the number of tickets left in the raffle.

enkoda · 17 Apr 2013 at 14:25

The chances of winning are 50%.

1 in 5, 5 in 25, etc, are irrelevant, you'll either win or you won't.

inogen · 17 Apr 2013 at 14:31

enkoda said:
The chances of winning are 50%.

1 in 5, 5 in 25, etc, are irrelevant, you'll either win or you won't.

Or from WillyNelson's POV he won or he didn't

Reaper 392 · 17 Apr 2013 at 14:49

geuben said:
Are you sure about that?

Example:

3 tickets are drawn in a raffle, what is the probability that you will have 1 winning ticket if:

a) there are 5 possible tickets and you have 1 ticket
b) there are 25 possible tickets and you have 5 tickets

Answers:

a) Odds of getting 1st winning ticket: 1/5
Odds of getting 2nd winning ticket: 1/4
Odds of getting 3rd winning ticket: 1/3

Total odds: (1/5)+(1/4)+(1/3) = 47/60 = 0.7833r

b) Odds of getting 1st winning ticket: 5/25
Odds of getting 2nd winning ticket: 5/24
Odds of getting 3rd winning ticket: 5/23

Total odds: (5/25)+(5/24)+(5/23) = 1727/2760 = 0.6257

Unless i'm being really stupid, that is not quite right. When you are looking into the second and third tickets, you need to account for the probability that the tickets before that weren't winners. I think this is the case because if there were four prizes in the first scenario, your method would result in a probability of greater than one which clearly isnt possible.

so for the 1 ticket in five scenario it would be:
chance that first ticket being drawn was yours
OR
chance that first ticket drawn was not yours AND second ticket drawn was yours
OR
chance that first ticket AND second ticket being drawn was not yours AND third ticket was.

so the maths should look something like this I believe

1/5 + (4/5 * 1/4) + (4/5 * 3/4 * 1/3) = 3/5 = 0.6

the fact that its 3/5 leads me to believe that there is a far simpler way of working it out in this scenario, but this was the most logical way I could think of to show

for the second scenario you have to work out the chances of winning AT LEAST one prize, which means you need to work out the chance of winning two prizes or three prizes as well. its far easier to work out the chance of not winning anything in this scenario and to take that probability away from one

so the chances of ticket one not winning AND ticket two not winning AND ticket three not winning are:

20/25 * 19/24 * 18/23 = ~0.495

so the probability of winning something in the second raffle if there are three prizes is ~0.505

as far as i can tell this is correct, but please let me know if i've done something stupid here

inogen · 17 Apr 2013 at 16:24

I'm sure the OP being a finanical analyst with a GCSE in statistics will be familiar with working using binomial coefficients. They're the key to working out the probability of events that aren't mutually exclusive, such as winning raffles with multiple prizes.

There's a good explanation here > http://math.stackexchange.com/questions/91998/probability-of-winning-a-prize-in-a-raffle

WillyNelson · 17 Apr 2013 at 16:31

inogen said:
It's future, present, or past tense, a mixture of all, some or none is irrelevant.

1/5 = 5/25

It's maths. You're confused.

What if I asked you, "I bought 5 raffle tickets yesterday, there were a total of 25 tickets, what was the probability that I won?". Would you be able to solve that?

Stop trolling. I said as much in the OP, I was just checking there wasn't something with the multiplication of chances that I'd overlooked. My past events comment stems from Martytoon's question...

Martytoon said:
But do you not have to consider the probability of profitability?

I replied that it is unlikley as I deal with things that have already happened
(cost/revenue), probability doesn't come into it.

Would you say to me "I paid £1 for a raffle ticket yesterday and won £5. What's the probability that I made a profit?" No, because it's a stupidly pointless question. Can you understand that...?

DaleTheWhale · 17 Apr 2013 at 16:39

^ Yes I can. I am now a financial analyst!