Groups

# 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?

8-)

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

Can we have the answer now please ?

Original Poster

Correct! ;-)

John

Original Poster

I've posted that Monty Hall problem before.

John

Switch your choice :thumbsup:

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

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

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%

switch

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

John

[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

1/3odds.. 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

2/3win 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!

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...

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

thengiven 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.

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