It’s been forever, it seems, since we downed a cold
one at Morty’s, but a quick visit last night did not
disappoint, in more ways than one. As usual, Alex
was holding court, over in the corner table.
Gather round me, boys, he began, and try to learn
something. And if it costs ya a quid or two, you’ll
remember it all the more.
With that, he took the four Aces from a deck of cards,
shuffled, and dealt them face down on the table. Now
one of you lads grab a couple bottle caps from the
floor and place them, one each, on two of these
here cards. Jamie obliged.
Now here’s the deal, Alex continued, there’s a certain
probability that the caps are sitting on cards of the
same color [red or black]. I’ll bet even money with
anyone who can say what that probability is.
Jamie was first to respond. It’s quite simple, ya see?
There are three cases. They’re sitting on black cards,
red cards, or mixed cards. The probability of the same
color is clearly 2/3.
You’ve been at the tap too long, laughed Ian, you
forgot that mixed cards can be red-black or black-red.
There are actually four cases, and the same-color
probability is 1/2. They either match, or they don’t.
Davey sat for a moment, stroked his bushy red beard,
and then walked over to Alex and whispered his answer
so none of the others could hear.
Given that only one of the boys had it right, who went
home that night richer than he came?
October 26th, 2010 | Category: 
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The last boy (assuming he got it right).
The first cap can be on any card, let’s just say it’s red because it doesn’t matter.
The three remaining cards each have 1/3 chance of getting the second cap. 2 of these cards are different in color than the first and 1 is the same. Therefore there is a 1/3 chance of the cards being the same and a 2/3 chance of the cards being different.
Close enough!
The correct odds are 1/3. The first cap picks the suit and then there is a one in three shot that the 2nd cap hits the same suit. The person who went home the richest, however, was Alex. He collected money from two and only had to pay out to one.
Nice job.