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Luckily...you have finally made it on the Joe Shmo giveaway show!
You have in front of you two identical treasure chests ( on the exterior ). I tell you that one chest contains 100 silver coins and the other contains 50 silver and 50 gold coins. You are then blindfolded and asked to pick a chest at random and draw a coin: Its a silver coin - its yours to keep, so you place it in your pocket. To your surprise I then give you a second chance! If you draw a gold coin you keep the entire contents of the chest; if not, you just get the coins you drew ( everyone walks away richer on the Shmo Show! )
What is the ( what I'm naming ) relative likelihood 𝑅 you draw a gold coin if you switch chests vs. stay for the next draw?
𝑅 = 𝑃( Gold | Switch ) / 𝑃( Gold | Stay)
Please hide your response so everyone get a chance to play!
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@joe-shmo saidWhoever has the grievance, please speak up. I'm all ears.
Luckily...you have finally made it on the Joe Shmo giveaway show!
You have in front of you two identical treasure chests ( on the exterior ). I tell you that one chest contains 100 silver coins and the other contains 50 silver and 50 gold coins. You are then blindfolded and asked to pick a chest at random and draw a coin: Its a silver coin - its yours to keep, so you pla ...[text shortened]... 𝑃( Gold | Switch ) / 𝑃( Gold | Stay)
Please hide your response so everyone get a chance to play!
@joe-shmo saidis this like the monty hall problem?
Luckily...you have finally made it on the Joe Shmo giveaway show!
You have in front of you two identical treasure chests ( on the exterior ). I tell you that one chest contains 100 silver coins and the other contains 50 silver and 50 gold coins. You are then blindfolded and asked to pick a chest at random and draw a coin: Its a silver coin - its yours to keep, so you pla ...[text shortened]... 𝑃( Gold | Switch ) / 𝑃( Gold | Stay)
Please hide your response so everyone get a chance to play!
- Joined
- 10 Dec 06
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- 8528
A warmup to the Shmo Show:
1) What is the probability you drew a silver coin on the first draw?
2) What is the the probability you chose the chest with 50 gold coins on your first draw?
3) What is the the probability you chose the chest with 50 gold coins on your first draw, given that you drew a silver coin?
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@lemondrop saidNot really, because the trick (which most people who pose it gloss over - Marilyn Vos "Savant" (in)famously didn't even understand that she'd done so) in that one is that Monty Hall knows what's behind the curtains. So, he actively changes the odds after the fact.
is this like the monty hall problem?
In this case, the odds aren't actively changed, but your knowledge about them is, and therefore the result is still counterintuitive.
It is, I rather think
And therefore, since it is given that you did pick a silver one,
Hold on, that's not right. It's almost right, but it ignores that you put the first coin in your pocket. The first three-quarters of the solution remain the same, but the last quarter turns out to be that
So the real odds are
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@shallow-blue saidReal close.
Not really, because the trick (which most people who pose it gloss over - Marilyn Vos "Savant" (in)famously didn't even understand that she'd done so) in that one is that Monty Hall knows what's behind the curtains. So, he actively changes the odds after the fact.
In this case, the odds aren't actively changed, but your knowledge about them is, and therefore th ...[text shortened]... cases is rather close to what I said before, but in both cases your odds are just slightly better.
P ( Stay | Gold ) = 1/3*50/99
P ( Switch | Gold ) = 2/3*50/100
R = P ( Switch | Gold ) / P ( Stay | Gold ) ≈ 2
"but in both cases your odds are just slightly better"
I don't agree with this statement above though...
The odds are significantly better if you switch. You go from 16.8% to 33.3%