The point lies in what Monty does when you choose a door. He deliberately opens a door that doesn't have anything behind it. Thus making sure that the 2/3-probability still lies with the door(s) you haven't chosen. I had my students try it out on eachother and it pays off to switch in two thirds of the cases.
I had no idea what the Monty Hall problem was. Upon looking it up, I think I can explain it:
Monty introduced NEW INFORMATION into the system once he exposed the door that was a zonk (he told the contestant which door NOT to choose). The contestant had NO new information on the door he/she chose, but new (and beneficial) information on the doors he/she didn't choose. To benefit from that new info, the logical choice was to switch.
If that still doesn't make sense, i can try to explain it differently.
Do you agree that when you choose your initial door, the probability of being right is 1/3? Baring a switcheroo behind the door, that probability cannot change. The car won't jump to or away from the door.
The other doors also have 1/3 chances. Until Monty opens one, now that door has 0/3 chances of being right. You door is still 1/3, we already established it can't change. There's now 1/3 unaccounted for. Where did it go? To the remaining door which brings it to 2/3.
The point lies in what Monty does when you choose a door. He deliberately opens a door that doesn't have anything behind it. Thus making sure that the 2/3-probability still lies with the door(s) you haven't chosen. I had my students try it out on eachother and it pays off to switch in two thirds of the cases.
I had no idea what the Monty Hall problem was. Upon looking it up, I think I can explain it:
Monty introduced NEW INFORMATION into the system once he exposed the door that was a zonk (he told the contestant which door NOT to choose). The contestant had NO new information on the door he/she chose, but new (and beneficial) information on the doors he/she didn't choose. To benefit from that new info, the logical choice was to switch.
If that still doesn't make sense, i can try to explain it differently.
Why isn't the choice to stay or switch independent from the first choice to choose one of the 3?
Do you agree that when you choose your initial door, the probability of being right is 1/3? Baring a switcheroo behind the door, that probability cannot change. The car won't jump to or away from the door.
The other doors also have 1/3 chances. Until Monty opens one, now that door has 0/3 chances of being right. You door is still 1/3, we already established it can't change. There's now 1/3 unaccounted for. Where did it go? To the remaining door which brings it to 2/3.
Ohhhhhhhhhhhhhhhhhh! I got it now. Thanks!