LogFAQs > #905503614

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Tyranthraxus
07/22/18 12:28:27 AM
#84:


kg88222 posted...
There has got to be a way where you can just pick from one box and eliminate all the ones where you pick from the box that has no gold balls from the start. It doesn't need to be that complicated. Just calculate the percentage of every time you pick from one of those 2 boxes and what the probability actually is after that.

Stop.

You are not picking a box.

You are picking a ball.

The ball just ends up being gold.

Think of it like this if it helps.

1. Pick a box.
2. Draw a ball from the box.
3. If it's silver, discard the experiment and start over at step 1.
4. If it's gold, how likely was it that you picked it from the box that has 2 gold balls versus how likely is it that you picked it from the box with one gold ball.

You are twice as likely to have grabbed it from the 2 ball box than the 1 ball box.

Because the two ball box has 100% chance of drawing a second gold ball, and the other box doesn't have any, the real question you're asking is "what is the probability that the gold ball I picked came from the 2 ball box?"

That's 2/3 because you're twice as likely to get it there as you are the one ball box.
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