> Yes I gathered, but in reality there's not an infinite number all produced in equal quantities.
Most of the McDonald's toys are made in equal quantities, and the quantity available dwarfs the quantity any one customer buys.
> clearly it must make some - if only 1000 of each toy were produced and 1000 customers took part, surely very few would have been lucky enough to get all 4 toy types at all
I don't think the odds change much in this case. 4 provides you with a very small chance from a bottomless pit -- 3/4 * 1/2 * 1/4 = .09375 chance of getting all 4 with with purchased.
It's slightly better if there's a small number, say, 4 of each, because you remove the ones you don't want from contention.
You have a 12/15 chance of the second not matching (3 toys remain that you don't want; and 4 toys each remain of each of the 3 kinds you want); then a 8/14 chance of the third not matching, and then a 4/13 chance of the fourth one not matching-- or a ~14% chance. So even when we say there's only 4 of each toy, the odds don't change -that- much.
Once we get to 1000 of each, the odds basically are the same as the infinite case. 3000/3999, 2000/3998, 1000/3997 are practically 3/4, 1/2, 1/4 -- ~.09389.
> as on average they could have only received 4
Well, we already know from the infinite case you need to buy more than 4 to have a good shot.
Most of the McDonald's toys are made in equal quantities, and the quantity available dwarfs the quantity any one customer buys.
> clearly it must make some - if only 1000 of each toy were produced and 1000 customers took part, surely very few would have been lucky enough to get all 4 toy types at all
I don't think the odds change much in this case. 4 provides you with a very small chance from a bottomless pit -- 3/4 * 1/2 * 1/4 = .09375 chance of getting all 4 with with purchased.
It's slightly better if there's a small number, say, 4 of each, because you remove the ones you don't want from contention.
You have a 12/15 chance of the second not matching (3 toys remain that you don't want; and 4 toys each remain of each of the 3 kinds you want); then a 8/14 chance of the third not matching, and then a 4/13 chance of the fourth one not matching-- or a ~14% chance. So even when we say there's only 4 of each toy, the odds don't change -that- much.
Once we get to 1000 of each, the odds basically are the same as the infinite case. 3000/3999, 2000/3998, 1000/3997 are practically 3/4, 1/2, 1/4 -- ~.09389.
> as on average they could have only received 4
Well, we already know from the infinite case you need to buy more than 4 to have a good shot.