A Wise Choice

[davar55]

You're given a choice of three doors, behind each of which is a prize --
one, an expensive car, the others, worthless tricycles. The car is
placed behind a random door. After you make a choice, one of the
other doors is opened revealing a tricycle. You are then given the
option to keep your original choice or switch to the other unopened door.
Assuming you want to win the car, should you stay or switch?

[R.D. Silverman]

Originally Posted by davar55

You're given a choice of three doors, behind each of which is a prize --
one, an expensive car, the others, worthless tricycles. The car is
placed behind a random door. After you make a choice, one of the
other doors is opened revealing a tricycle. You are then given the
option to keep your original choice or switch to the other unopened door.
Assuming you want to win the car, should you stay or switch?

Oy vay. Not again.

[ewmayer]

Where's Marilyn "Self-Proclaimed World's Smartest Woman" Vos Savant when you need her?

For that matter, where's Monty Hall?

[davar55]

I should have realized this has been discussed, but I think it
was quite a while ago. If it's not worth it, then ok, let it go.

[ewmayer]

Anyway, what have you got against tricycles? A very underrated form of transportation, sure to come back into vogue once U.S. gas prices hit $5 per gallon later this year.

[Uncwilly]

Originally Posted by ewmayer

Anyway, what have you got against tricycles? A very underrated form of transportation, sure to come back into vogue once U.S. gas prices hit $5 per gallon later this year.

A major US newspaper had an article on 3-wheeled motorcycles recently. It seems that in some areas, riders need not have a valid motorcycle license to ride them.

[davieddy]

Originally Posted by davar55

After you make a choice, one of the
other doors is opened revealing a tricycle.

Was there the chance of it revealing the car?
I am undeterred by the poohpoohing tone of the
initial response

[davar55]

Originally Posted by davieddy

Was there the chance of it revealing the car?

No. A tricycle was inevitable.

(I have nothing against tricycles.
They certainly are fuel-efficient and child-friendly.)

[davieddy]

Originally Posted by davar55

No. A tricycle was inevitable.

Thanks. I had anticipated the follow up question where
one of the remaining doors is opened at random.

I hope no-one posts a link to the previous discussion or anything
else before appropriate thinking has taken place in this thread.
(See discussion of googling puzzles in your "Count the triangles")

[Brian-E]

Was it agreed before the first door was chosen that the next thing that would happen would be the opening of another door revealing a tricycle?
Or could the original choice of door have influenced what happened next?

[davieddy]

I choose door A and there are 4 outcomes:

The car is in A and you open door B (1/6)
The car is in A and you open door C (1/6)
The car is in B and you open door C (1/3)
The car is in C and you open door B (1/3)

You swap. (You now know which of the two not to swap with!)
In Bridge this is known as the "Principle of restricted choice".

The chance of the car being behind door A remains 1/3, but that
now leaves 2/3 for the car lying behing the unchosen door.