Maths boffins Odds and Probability

[Bald-Eagle22]

Guys need some help to work the last part of this out, probability was not my strong point at school.

Scenario. Literally a bag with some numbers in it and the same number gets pulled out three times in a row three weeks apart.


1. 17 different numbers go in the bag and i Pull out number 6
2. 18 different numbers go in the bag and I pull out number 6
3. 17 different numbers go in the bag and I pull out Number 6


I was 8th in turn to pull a Number out and each number that was pulled out was not put back in the bag .

Odds of this happening are ?

 

[Bald-Eagle22]

With the current amount of information, completely unknown, you mention 17/18 numbers go into a bag, are they all numbered 6 or are they numerically numbered 1-17/18, you mention the number pulled out isn't put back but take out 3 6's in the 3 scenarios are there multiple drawings from the same bag in one weekly lottery or are these three seperate lotteries with a singular 6 in each time.

17 or 18 different numbers ( 1 to 17/18 )each drawn out by different people and they don’t go back in the bag ,I’ve been 8th in turn each week

Assuming that we are talking 3 seperate lotteries, the chances that a 6 comes out is the same as any other number (assuming 1 of every number is in the bag, i.e. 1-18). This also assumes that the 6 is drawn first, is this in the middle of a draw, do we draw how many times per lottery, if we pull 7 or 8 numbers per lottery then the chances of seeing a 6 every time is relatively high considering we are withdrawing half the bag almost.

Its 1 draw per person , ie 17 numbers 17 people each get 1 draw . Same happened three weeks on the trot !

One final note is that you mention you was 8th in turn on a bag with 17/18 numbers, that would imply the chances of you drawing a 6 on each time would have been 1/9, 1/10 and 1/9 for each weekly draw, they cannot (reasonably) be multiplied as they are completely independent events and therefore the chance of you drawing a 6 in next weeks draw in the same position (e.g. 8th out of a bag of 18) is going to be once again 1/10. Unless you are placing a bet on drawing a 6 for 3 weeks in a row, only then would it be reasonable to infer the odds of such a thing.

The human mind is a wonderful thing and sees many great patterns but when it comes into statistical modelling it's dull as dishwater and attempts to see statistical correlations (especially in random distributions) that simply do not exist.

Was just wondering if it had any bearing .

 

[Bald-Eagle22]

Wouldn't you just multiply the odds?

17*18*17= 5202/1

What I thought but can’t be that simple .

 

[Bald-Eagle22]

No



You're over complicating things; if it's a fair process then the person in position 1 has the same chance of being allocated the 6 as the OP or indeed the person in position 17.

You don't need to add extra steps here to calculate that that is 1/17 for a draw where there are 17 numbers and he's allocated 1.

Think about it

positon 1: 1/17
positon 2: 16/17*1/16 = 1/17
position 3: 16/17*15/16*1/15 = 1/17

and so on...

You just need to know he's getting 1 number allocated at random from 17 as he hasn't asked anything about his positon or told us how that's allocated.

Position is called by the organiser who takes names on a list from the prior week , your name then gets called out on that list so it’s probably going to stay the same each time until I don’t attend ( it’s a sporting event of sorts ).

 

[Bald-Eagle22]

Yeah, that's true.

I guess it depends what the OP is asking as he's not clarified... "I got a 6 this week, what were the chances of that?": 1/17 "A 6 was also what I got the week before and the week before that too, what were the chances of all three draws giving me a 6" etc...

Yes exactly this thanks .

OK so I guess there isn't really anything being asked about the positon ergo it's just one of the two answers above depending on whether you're asking what were the chances of you specifically getting a 6 in the three draws or, as per @Grrrrr 's answer re: what are the chances you simply had 3 numbers in a row. I guess perhaps it's actually that which you're asking, you've noticed the same number three times ergo you're surprised.