Losing Your MarblesProbability puzzles require you to weigh all the possibilities and pick the most likely outcome.
There are 3000 marbles in a machine - 1000 red, 1000 green, and 1000 blue. The machine churns out a random number of marbles into a bag (any number from 1 to 3000), without letting you see the inside, so you don't know how many of each colour, or in total, there are. What is the probability, without looking into the bag, that you will pick out a red marble?
HintThe bag is only an intermediary step... The answer is the same even when weighing out all the cases, because you don't know what marbles the machine churned out.
AnswerThe probability is 1/3. The bag is an intermediary step intended to mislead you into thinking it's something else.
Even if the machine does churn out only blue and green marbles and the probability directly from the bag is 0%, you don't know that, and it could have picked out only red marbles, in which case the probability is 100%. All the cases average out to 1/3.
The probability is the same as if you picked one directly from the machine.
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