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# Aces and Joker puzzle

You have a full 52 deck of cards plus a Joker spread out and face down on a table in front of you. You cant tell which card is which by looking at them or otherwise. You now start flipping cards over one by one, you turn each card only once. What is the percentage probability that you turn over all four Aces before you flip over the Joker?

24%?...

5% chance ?

20% :thumbsup:

8-)

cupracooper;1666587

20% :thumbsup:

Forget the other cards; 4 aces, 1 joker = 20% chance.

16 to 1 (16/1) ?

Original Poster

cupracooper;1666587

20% :thumbsup:

Correct! ;-)

Here's a slightly different one, similar idea though - you have three cards face down, one of which is the queen (the other two are not, simple as that). The challenge is to find the queen so you choose a card but it's not revealed yet. One of the other two non-queen cards is turned over and revealed leaving you with your original choice and one other card still face down. Now you have the choice to stick with your original choice or change, which do you do to give you a higher probability of winning?

John

Original Poster

Johnmcl7;1667567

Here's a slightly different one, similar idea though - you have three … Here's a slightly different one, similar idea though - you have three cards face down, one of which is the queen (the other two are not, simple as that). The challenge is to find the queen so you choose a card but it's not revealed yet. One of the other two non-queen cards is turned over and revealed leaving you with your original choice and one other card still face down. Now you have the choice to stick with your original choice or change, which do you do to give you a higher probability of winning?John

I've posted that Monty Hall problem before.

As have I but it's still a good puzzle

John

Johnmcl7;1667567

Here's a slightly different one, similar idea though - you have three … Here's a slightly different one, similar idea though - you have three cards face down, one of which is the queen (the other two are not, simple as that). The challenge is to find the queen so you choose a card but it's not revealed yet. One of the other two non-queen cards is turned over and revealed leaving you with your original choice and one other card still face down. Now you have the choice to stick with your original choice or change, which do you do to give you a higher probability of winning?John

Toonami;1666713

8-)Forget the other cards; 4 aces, 1 joker = 20% chance.

actually to hit all 4 aces and miss the joker with 5 cards the probability is 30%

GMC1001;1668356

took me a while to understand the question but it makes no difference as you dont know what card you have chosen as it is not turned over yet. so you now have 50% chance in getting the Queen so switching wont make a difference in probability

kk_cheung;1668424

actually to hit all 4 aces and miss the joker with 5 cards the … actually to hit all 4 aces and miss the joker with 5 cards the probability is 30%

Definately 20%

Odds are 4/5 you'll get an ace 1st time (4aces 1joker)
and then continue as 3/4, then 2/3 then 1/2

So (4/5) * (3/4) * (2/3) * (1/2) = 1/5 or 20%

oops my bad i put 3/3 in my calculations instead of 2/3

kk_cheung;1668470

took me a while to understand the question but it makes no difference as … took me a while to understand the question but it makes no difference as you dont know what card you have chosen as it is not turned over yet. so you now have 50% chance in getting the Queen so switching wont make a difference in probability

switch

kk_cheung;1668470

took me a while to understand the question but it makes no difference as … took me a while to understand the question but it makes no difference as you dont know what card you have chosen as it is not turned over yet. so you now have 50% chance in getting the Queen so switching wont make a difference in probability

I won't say any more yet but it's not 50% probability.

John

kk_cheung;1668470

took me a while to understand the question but it makes no difference as … took me a while to understand the question but it makes no difference as you dont know what card you have chosen as it is not turned over yet. so you now have 50% chance in getting the Queen so switching wont make a difference in probability

[SIZE="4"]SWITCH definately :thumbsup: = 2/3 chance of win[/SIZE]

Ok this is slightly more complex to explain than the last one :?

Your inital choice is a 1/3 odds.. Easy.. if you stick with your choice you odds remain the same.

Picked Queen & stick = Win
Picked Other1 & stick = Loose
Picked Other2 & stick = Loose

by being shown a losing card (other1 or other2) and swaping you increase your chance to 2/3 win because if you orginally picked....

Picked Queen & you swap = Loose
Picked Other1 & you swap = Win
Picked Other2 & you swap = Win

So you win 2/3 of time, therefore your twice as likely to win by swapping!

but it says that you dont know your card, so there is at the moment of decision, one losing card turned over, one card picked but not known, and also another card faced down.

so now there are only 2 cards that are faced down one correct and one incorrect and you have chosen one, which makes it 50% chance

i think thats what the question asks anyway...

kk_cheung;1670583

but it says that you dont know your card, so there is at the moment of … but it says that you dont know your card, so there is at the moment of decision, one losing card turned over, one card picked but not known, and also another card faced down.so now there are only 2 cards that are faced down one correct and one incorrect and you have chosen one, which makes it 50% chancei think thats what the question asks anyway...

Look it up on the web; it is a well known puzzle. If I remember you have a 1/3 chance of picking the right card with your initial choice, however one of the unknown cards is turned & shown to be wrong, you are then given the chance to stay with with your card or pick the other unknown card and the question is should you switch?

The odds that your card is right remain at 1/3, as you hadn't seen any card turned however, the odds that the other card is right have changed favourably from 1 in 3 to 2 in 3 as you know that one of the other cards is wrong & you wouldn't now pick that card. At the initial choice stage you may have picked that card.

I think the confusion is that you don't choose the "non-queen" card to reveal. Someone else (who knows what the cards are) turns over the non-queen card.

It's definitely better to switch (this was on the Royal Institute Christmas Lectures around 10 years ago!!).