[Puzzler] A Pair of Aces

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Mike
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[Puzzler] A Pair of Aces

Postby Mike » Thu Jul 20, 2017 11:44 am

This is to follow up , because they work out the same muscles:

You have four cards: Ace of Spades, Ace of Hearts, 2 of Spades, 2 of Hearts.

The four cards are shuffled, and you draw two cards at random.

Two scenarios:

1) What is the chance that you drew a pair of Aces if you know that at least one card is an Ace?

2) What is the chance that you drew a pair of Aces if you know that one card is the Ace of Spades?
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Zen
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Re: [Puzzler] A Pair of Aces

Postby Zen » Thu Jul 20, 2017 3:46 pm

I'm not sure, but I can tell you that the chances of you having a pair of aces if you don't have at least one ace is 0%.

Okay, more seriously...

If you know one card is an Ace:



If you know 1 card is the Ace of Spades.

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Mike
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Re: [Puzzler] A Pair of Aces

Postby Mike » Thu Jul 20, 2017 4:08 pm

Zen wins all the candy!
All I know is my food tastes better when I take my food-tastes-better pill.
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Re: [Puzzler] A Pair of Aces

Postby Zen » Thu Jul 20, 2017 4:59 pm

Well, I should be able to do this stuff... I used to use versions of combinations and permutations for my grad school research on the effects of superficial similarity of novice problem solving... Not that I had to do the problems, but I looked at them a lot... a WHOLE lot!
"The lines between kindness, apathy, and thickheadedness can be very thin." - Nakatani Nio Sensei
“The direction of escape is toward freedom. So what is ‘escapism’ an accusation of?” - Ursula K. Le Guin
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Re: [Puzzler] A Pair of Aces

Postby Phoebe » Thu Jul 20, 2017 10:40 pm

Ok if you know it's the ace of spades
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Eliahad
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Re: [Puzzler] A Pair of Aces

Postby Eliahad » Thu Jul 20, 2017 10:55 pm



Phoebe, it has to do with counting the number of possible cases, and not just the cards left in the draw pile. If you lay out all the possible outcomes (since this is small enough to do), you will see that there are more possible outcomes than just the next draw.

Your feelings about this puzzle remind me of a different one. The shell game probability puzzle never sat well with me. (The one where the huckster puts a pea under one shell. Mixes them up, and then reveals one of the shells that doesn't hold the pea. The odds of picking the correct shell do NOT increase to 50%, but even after seeing the explanation, it still bugs me.)
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