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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If each choice is made independently of the previous choices (meaning the previous choices do not affect the probability of the next choice), then the probability of choosing the same number each time is simply the probability of choosing that number once, raised to the power of the number of choices. For example, if you’re choosing a number between 1 and 10, and you choose the number 7 with probability 1/10, then the probability of choosing 7 three times in a row is (1/10)^3 = 1/1000.
Because your dealing with 2 events, the choice and the series, which contains the choice, each successive choice make the chance more remote of getting the same number. The probability on choice 500 would be (1/10)^500.
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