[CV102] Aces and the Joker

Aces and the Joker is a puzzle in Professor Layton and the Curious Village.

Puzzle

You've scattered a deck of 52 cards and one joker facedown on a table so that you don't know which card is where.

Next you start turning the cards over one by one. Assuming that you can't flip the same card twice, what are the percentage odds that you will turn over all four aces before you turn over the joker?

Hints

Click a Tab to reveal the Hint.

Out of 53 cards, four are aces. Each time you flip a card, the probability of turning over an ace increases...but you really don't need to work out any of that.

Think about what you can do to eliminate other variables to consider.

If you distill this question down to its simplest form, it's just asking you how likely it is you'll flip over four aces in any order before you turn over the joker.

The other 48 cards have nothing to do with the problem.

OK, let's lay it all out on the table, so to speak.

There are five cards that actually matter in this puzzle. Of those five, the joker has to come last. What's the probability of flipping the joker after the other four cards?

Solution

Incorrect

Too bad.

Don't worry! You don't need to bother with complex calculations to solve this one!

Correct

That's right!

While it may seem like you need to take other cards into account, no card in the deck, save the joker and four aces, plays any part in calculating the percentage.

Knowing that you only have to deal with five cards in your calculations, the rest is easy. You have five cards to flip, and you need one of those five cards to be last. So your answer is one out of five, or 20 percent.

A big thanks to http://professorlaytonwalkthrough.blogspot.com

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Puzzle

Hints

Solution

Incorrect

Correct