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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There’s no such thing. All 6s is the same as all different in terms of likelihood to be picked.
This is because lottery numbers are sampled “with replacement”. This means even if the lotto picked a 6 for the first number, the same 6 is eligible for the second number, etc. Further the numbers are picked independently.
In games where items are picked “without replacement”, the events are not independent – each selected item influences the possibilities of the next. So for example in those games you will never see duplicates. An example of this is if you have labeled numbers and you pull them out of a bag. Each number you pull is now no longer in the bag.
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