Was watching a podcast recently where a girl called another girl dumb for choosing all 6 for a lottery ticket saying that after one 6 is chosen, the probability of each subsequent 6 being chosen decreases. I.e you’re better off choosing 10 random numbers than 10 6’s.
The other 2 in the podcast called the girl an idiot because each six is chosen separately. So the probability of arriving at all 6 is the same as any other combinations. This seems to make sense to me. Rolling 10 dice, the probability of one 6 doesn’t magically effect the other result of the other di.
However I seem to vaguely remember being taught something similar to the supposedly idiot girl when I was a kid.
So basically, who’s right and why?
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First, I’m not sure where these people are playing the lottery but either they all don’t know what they are doing or it’s a very weird lottery.
In most areas there is no repetition of numbers in the lottery. In other words you can only pick each number once. You could play multiple times in the same lottery (ie buy multiple combinations of numbers) and have one six in each one, but you can’t purchase just one draw and have two, let alone six sixes.
Ignoring that it would depend on how this weird lottery is being done.
With replacement, meaning after you draw a ball (or however the number is chosen) you put it back and draw again then there is no difference in the odds between drawing say six 6’s or the sequence 1, 2, 3, 4, 5, 6.
If you don’t replace the already chosen number, then yes the odds would be worse because there are now less 6’s available to draw. In the case of most lottery’s that less 6’s is actually zero 6’s because there is only one of each number to begin with.
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