The Breakroom > The Water Cooler

Bit of a maths puzzle

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andyf:
 :scratch: :scratch: :scratch:
I'd switch to door 2.

To avoid confusion with the existing numbers, there's one door with a car behind it and another two hiding goats - call those goat doors X and Y.

There are 3 possible scenarios:
1. My first choice was the door which hides the car. When offered my second choice, I switch to another door (either X or Y) so I lose.
2. My first choice is door X which hides a goat. If when offered my second choice, I switch to door Y, I win  (the host having exposed the other goat before offering me that second choice).
3. My first choice is door Y which hides a goat. The host is forced to open door Y and show me the other goat. If I switch when offered my second choice, I win the car.

In the first of those scenarios, I lose, but in either of the other two I win, so the odds are 2 to 3.

If I don't switch when offered my second choice, then:
1. I win - I choose the right door first time, and stick with it.
2. I lose - I choose door X first time round and stick with it, but it hides a goat.
3. I lose - I choose door Y first time round and stick with it, but it hides a goat.

In the first of those scenarios I win, but in either of the other two I lose, so the odds are only 1 in 3 when I stick with my original choice.

QED (I think!)

Andy
 

cidrontmg:
Yes, like Andy said, changing ones mind in this situation gives better odds, if you want the car. I already have a car, though, so IŽd  be happier with the goat....    :lol:

z3t4:
Just noticed that Wiki seems to be in a state of some disquiet re the Monty Hall problem. As with most Maths stuff, it does seem to cover it very well, IMHO.

Goats are cute.

John

kvom:
The goat problem is similar to a principle in bridge called "restricted choice".  Assume your holdings in a suit is Axxxx vs K10xx.  As declarer you play the A and RHO plays the Q or J.  It is 2-1 to finesse when playing towards the K10.

jim:
the earth/string one is one of my favorites.

the version i've heard was "how longer would the string be if it was lifted up an inch?" i've seen very clever people resorting to calculators to prove its more than a few inches!!

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