OK, there seem to be a few stats. bods. here so I have a niggling question to ask.

OK, each lotto ball has an equal chance of being picked, but also each lotto ball is a certain colour.

So for argument's sake let's say 28 is picked, which is a pink ball. Now, my brain tells me that each remaining ball has an equal chance of being picked. However, it's also telling me that a pink ball is less likely to be picked next time.

That's my dilemma. Please help.

Okay, what exactly are you asking?

You are correct in thinking that the probability of a pink ball being picked next will be lower than the others. But what you're getting at beats me

How can it be less likely that a pink ball will be picked again if each ball still has a 1/48 chance of being picked?

That's my question.

It's not an equal chance, if you think about it. if there are an equal number of balls of each colour in the pot, then you pick out say a pink ball, that means there are slightly less pink balls left in the pot than balls of every other colour. So there is a slightly less chance than average that the next ball you pick out will be the same colour.

Simplify the model a bit. You have 50 balls, 10 balls each labelled A, B, C, D and E. You pick out a ball, labelled B. You now have 49 balls left in the pot :-

10 labelled A
9 labelled B
10 labelled C
10 labelled D
10 labelled E

So if you look at the balls you have left, you have a 40 in 49 chance of picking out a ball that isn't labelled B and a 9 in 49 chance of picking out a ball that is labelled B. So you have much more chance of picking out a different colour than the same colour. It's roughly 4 times more likely, in fact.

The numbers get more complicated as you pull more balls out but, essentially, you will usually have more chance of pulling a different ball out than a similar one.

Fundamentally it's not like tossing a coin. When you toss a coin, it doesn't actually matter whether the last time you tossed a coin it came up heads or tails - the chances are still 50/50. The system resets each time. In this case, you're changing the odds slightly each time you pick a ball, because you're not resetting the system each time.
There's actually a specific probabalistic term for chances that are always the same as oppose to chances that cheange depending on how many times you've taken the bet. But I can't remember what it is .


Jon

Each remaining ball (number) has a 1/48 chance, but the pink balls have less chance than any of the others, purely because there are fewer of them at that time, the more pink balls that are removed, the less chance of a pink appearing.

because the balls no longer have a 1/48 chance unless the ball is replaced. They now have a 1/47 chance and yes, it's less likely to be a pink ball next time.

If the ball is replaced after being selected then all the balls are still 1/48 and all colours are equally likely.

Hate to burst your bubble, there's 49 balls in the lotto We've removed one, hence the 1/48

But HOW!? Seriously? If each remaining ball has an equal chance (you can't see them, so surely each ball has the same chance of being picked? E.g. 1/48 instead of 1/49), and yet you're telling me that it's less likely a pink ball will be picked, even though each remaining ball seems to have an equal chance.

Aren't the two mutually exclusive? Am I making any sense at this point?

Wait, so you're telling me that I shouldn't look at it as 1/48 for each ball, but rather figure the odds according to which group the ball is in?

So wouldn't that technically make the winning combination of 1,2,3,4,5,6 much less likely than picking numbers out of each coloured category?

Basically, the probability of picking a number is 1/48. (i.e. chance of picking 25 next is 1 in 48).

The probability of picking this number OR that number (i.e. probability the next ball will be 21 OR 25) is 1/48 + 1/48 = 2/48 = 1/24.

The probability of picking a pink ball next (remaining pink balls are 21, 22, 23, 24, 25, 26, 27, 29, 30) is the same as the probability of picking 21 OR 22 OR 23 OR 24 OR 25 OR 26 OR 27 OR 29 OR 30.

i.e. 1/48 +1/48 + 1/48 + 1/48 + 1/48 + 1/48 + 1/48 + 1/48 + 1/48 = 9/48 = 3/16

So, the more numbers that can be chosen that are "correct" the greater the probability of choosing them.

OK, so that wasn't too basic. Hope it makes sense though.

I forgot the next part.

OK, let's look at the yellow balls (1, 2, 3, 4, 5, 6, 7, 8, 9, 10). The probability of picking a yellow ball is the probability of picking any one of these 10. i.e. 10/48

10/48 is a larger probability than 3/16 (use a calculator to get decimal versions). Therefore there is a higher probability of picking yellow than there is pink.

Your point about 1, 2, 3, 4, 5, 6...

Take 1, 2, 3, 4, 5, 6 and compare it to 3, 14, 25, 26, 34, 47.

The probability (P) of picking the first numbers (in any order as order doesn't matter) is...

P of 1 or 2 or 3 or 4 or 5 or 6 (for the first ball, let's say 3)
and P of 1 or 2 or 4 or 5 or 6 (for the second ball, 2)
and P of 1 or 4 or 5 or 6 (and so on...)

This comes out to 1/13983816

similarly the P of the second list is...

P of 3 or 14 or 25 or 26 or 34 or 47
and ... (you get the idea)

This also comes out to 1/13983816

All 6 number combinations in the lottery have the same probability of appearing.

So you're telling me that, in fact, the two aren't mutually exclusive, but rather, there's a slightly higher chance of a non-pink ball being the "correct" number (i.e. next draw)?

Okay, you put your hand in a bag of sweets and pull one out at random.

There's 4 red, 5 blue and 10 green, which colour is more likely to appear? The green, because there is a greater number of greens, this is little extreme, but the principal's there.

Yes, see the edit of my post for more stuff

OK, I *think* I finally have it sorted in my head. However, this has lead to a new problem,

If each time you pick a white number (1-10) it makes the next pick less likely to be a white, how can 1,2,3,4,5,6 have the same chance as 2,12,24,26,47,49 (or whatever) of being the winning combination?

EDIT: Oli, I know you addressed this in your post, but it was so confusing I'm going to ask you to make it really, really simple for us village idiots.

If the object was to match the colour of each ball that was drawn then yes it would make sense to take one of each colour. As soon as a ball is chosen then the probability of the next ball being the same colour drops.

BUT it doesn't mean that just because 28 was chosen first that 25 becomes less likely to be chosen. The colours and the numbers ARE mutually exclusive in terms of probability but removing a ball will affect the numbers AND colours because each ball has a number AND a colour.

However, the colours are purely there to make it look more attractive.

The numbers are the things you have to match. Not the colours.