> There are three boxes:
> – a box containing two gold coins,
> – a box containing two silver coins,
> – a box containing one gold coin and one silver coin.
>
> Choose a box at random. From this box, withdraw one coin at random. If that happens to be a gold coin, then what is the probability that the next coin drawn from the same box is also a gold coin?
My thinking is this… Taking a box at random would be 33% for each box. Because you got one gold coin it cannot be the box with TWO silver coins, therefore the box must be either the gold and silver coin or the box with two gold coins. Each of which is equally likely so the chance of a second gold coin is 50%
I understand that this is a veridical paradox and that the answer is counter intuitive. But apparently the real answer is 66% !! I’m having a terrible time understanding how or why. Can anyone explain this like I was 5?
In: Mathematics
If you pull out a gold coin, there’s only two possible boxes, but there were two random events that got us here.
| GG | x | SS | x | GS | x
— | — | — | — | — | —
1/3 | x | 1/3 | x | 1/3 | x
G | G | S | S | G | S
1/2 | 1/2 | 1/2 | 1/2 | 1/2 | 1/2
1/6 | 1/6 | 1/6 | 1/6 | 1/6 | 1/6
This is where we come in. We can see there are 6 ways we could have gotten here, but only 3 of those have had us pull a gold coin. If we just look at those 3, 2 of those came from the gold box, and one came from the mixed box. Therefore, we have a 2/3 chance for the gold coin to be in the box, and a 1/3 chance for there to be a silver one.
Latest Answers