"21" explains the Monty Hall problem

The character, Ben Campbell, from the movie "21" explains the Monty Hall problem.

• Category

  Education

[lavatramp]

Surely once 2 doors are remaining the probability is reset to 50/50. Your choice to stick with your original option is as much a choice as it would be to change.

[SalomeSchmidt]

Hmm - or rather: when you pick first, chances are 66%, that the car behind one of the other 2 doors. If one of these two is taken away, this likelyhood remains but it is now represented by only one remaining door.

[SalomeSchmidt]

but, on the other hand - if you had originally chosen number 2 (instead of number one) - and were then also shown number 3 as being a goat, you also should - for statistic reasons- do the switch. So if 2 persons play against each other go for different doors and both do the switch, both have a likelyhood of 66% to win - but only 50% of them will win...

[koal1ify]

Oh! I think I get it now. The only way you don't win when switching is if your first pick was the car and that only happens 1/3 of the time.

[Dragonninjas11]

Well originally the chances of winning were 33%, and the chances of losing were 66%. And so when the host reveals a goat, you have a 2/3 chance to win. This is because you originally only had a 33% chance of picking the car first, than the chance you had of picking the goats. So if you were to pick one of the goats, the host shows you another goat, and if you take the switch, then you win. You pick either goat, and take the switch, then its 66%, and you will win the car.

[koal1ify]

I feel so stupid. He reveals one goat which leaves a goat and a car in the last 2 doors. I don't see how 66% is gotten from that.

[DivinationByEntrails]

66 2/3%

Be precise.

[HumptyDumptyOakland]

Granted this video does a terrible job of explaining the problem, but if you look at some others or simply google Monty Hall you'll see that switching doubles your chances of winning the prize - from 1/3 to 2/3. And it's BECAUSE the host can only reveal a goat