You’re playing a card game entitled “Find the King”. 5 cards are on the table face down, 4 of them are Queen, and of course 1 King. You select card number 1, the dealer then flips 3 cards over and they are all Queens (card numbers 3,4,5). So you are now left with cards (1 and 2), He then says to you: ‘Do you want to switch to card number 2?’ Is it to your advantage to take the switch? And what is the probability card number 2 is the King?
2006-12-22 03:54:01 · 16 answers · asked by Jeff 2 in Science & Mathematics ➔ Mathematics
I created this modified version of the Monty Hall some years back, to help others understand how to solve and understand these types of problems using Bayes's Theorem of Conditional Probabilities. I would give a more indepth answer but I have limited space.
Good answer Sep_n
Yes - you switch the card. There is a greater chance it's the 2nd card than the first.
In the beginning, there was a 20% chance you were right (1 of 5 cards). Now that three of the other four cards were revealed as Queens, there is an 80% chance card 2 is a King and still only a 20% chance card 1 is a King.
2006-12-22 06:04:10 · update #1
Yes, it is now to your advantage to switch.
"sep_n" has the correct probability.
2006-12-22 04:04:04 · answer #1 · answered by J-Mo 2 · 0⤊ 1⤋
This is a version of the Monty Hall problem. There is extensive work on this on the net just google Monty Hall problem for a sample.
OK When you pick initially your chance of having the winning card is 1/5
When the dealer takes away three non kings you are left with the situation it was 1/5 that my card is a king originally. It wasnt it positions 3 4 and 5 there fore there is a 4/5 chance that it is in position 2 so you should swop.
However there is a big caveat here.
Lets say that the rule is the dealer knows where the king is and cannot turn that card over.
So once you've picked your card if it isn't the king there are only three cards he can turn over leaving the king either covered by you 1/5 chance or left uncovered 4/5 chance.
Here you are using his knowing where the king is to give you information and change your chance of choosing the king.
However there is an alternative. He may not know where the king is and turned three cards at random. If he turns the king who knows what happens it actually doesn't matter.
He picks three cards at random and they are all queens. This then does not make it an advantage to switch. Because he has no knowledge of the king's position he cannot give you any information so you can gain no advantage by swapping or not
2006-12-22 04:10:23 · answer #2 · answered by Selphie 3 · 0⤊ 1⤋
Yes - you switch the card. There is a greater chance it's the 2nd card than the first.
In the beginning, there was a 20% chance you were right (1 of 5 cards). Now that three of the other four cards were revealed as Queens, there is an 80% chance card 2 is a King and still only a 20% chance card 1 is a King.
You switch the card.
2006-12-22 03:57:09 · answer #3 · answered by sep_n 3 · 3⤊ 1⤋
This isn't entirely clear from the question, but if the dealer knows ahead of time where the king is and flips 3 cards that he knows are NOT the king, then you should switch. The switch will get you the king 80% of the time.
Your question is a variation on the "Let's Make a Deal" puzzle. Say, after you pick a door, the MC then shows you a different door that does not have the big prize. (The MC knows this.) Again, you should switch. Here, the odds are 2 to 1 in your favor that you will switch to the big prize.
2006-12-22 04:09:58 · answer #4 · answered by Anonymous · 2⤊ 0⤋
Well if it's not 50/50 you got me! I have no idea why it wouldn't be.
Edit: HAHAHA you are actually saying there is an 80% chance card #2 is King?? That is so NOT TRUE!! Try this experiment yourself and you will see that it is actually 50/50. This is nonsense and not an accurate representation of the Monty Hall Problem.
The critical detail you left out is that the dealer knows which card is the King and flips over three cards that aren't the king. If the player is aware the dealer knows the location of the king and must flip over three cards that are NOT the king, then it is to the player's advantage to switch.... GOD... "modified version of the Monty Hall problem".. ha ha ha
2006-12-22 03:56:48 · answer #5 · answered by scruffy 5 · 0⤊ 2⤋
Initially, you had a 1 in 5 chance of finding the king. With three of the cards being flipped over, revealing 3 queens, your chances of finding the king has increased to 1 in 2. Thus initially, you had a 20% chance of finding the king, now you have a 50% chance of finding the king. So yes, it is in your best interest to pick again.
2006-12-22 04:01:27 · answer #6 · answered by frich_27 2 · 0⤊ 3⤋
3-1
2006-12-22 04:54:54 · answer #7 · answered by Anonymous · 0⤊ 1⤋
The odds are 50/50 that the king is card number 2 but card number 1 has the same odds, there is no apprciable advantage.
2006-12-22 04:02:37 · answer #8 · answered by ikeman32 6 · 0⤊ 2⤋
no advantage, probability 1/2.
2006-12-22 04:55:20 · answer #9 · answered by rwbblb46 4 · 0⤊ 1⤋
50/50
2006-12-22 03:56:50 · answer #10 · answered by Anonymous · 0⤊ 1⤋