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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The key issue at hand is “independence” of the observations.
The first girl is making an assumption that the probability of getting a second six is affected by whether or not you got a six on the first draw.
The other two are making the opposite assumption, that each draw is unaffected by the results from the others.
If you’re drawing numbered golf balls out of a bowl without replacing them then the first girl would be right. There are only so many “6” golf balls in the bowl and removing one makes it less likely to be drawn in future rounds.
However, if the observations are independent, such as rolling a die a bunch of times, then the other two girls will be right.
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