So there are 3 doors. Behind 2 of the doors there's nothing but behind 1 there is a nice shiny lambo . Now you have to pick a door. After you do that The presenter ones one of the doors and shows a door that is empty. Now you are left with 2 doors. One you chosen and one other that is left. The presenter gives you a chance to either switch door or stick with your one. What do you do ? Which gives a higher chance of winning ?
So there are 3 doors. Behind 2 of the doors there's nothing but behind 1 there is a nice shiny lambo . Now you have to pick a door. After you do that The presenter ones one of the doors and shows a door that is empty. Now you are left with 2 doors. One you chosen and one other that is left. The presenter gives you a chance to either switch door or stick with your one. What do you do ? Which gives a higher chance of winning ?
When you first choose your door, there are 2 empty doors and 1 door with the prize in it. Thus, the chances of you having chosen the correct door is 1/3. Now that one of the empty doors has been removed, there is only 1 door with the prize in it and 1 empty door. The chances of you having chosen the prize is still 1/3, which means the chances you picked an empty door are 2/3. Since you get to switch doors, if the chances you picked an empty door are 2/3 then when you switch you have a 2/3 chance of winning the prize, compared to a 1/3 chance if you stay with the original door.
When you first choose your door, there are 2 empty doors and 1 door with the prize in it. Thus, the chances of you having chosen the correct door is 1/3. Now that one of the empty doors has been removed, there is only 1 door with the prize in it and 1 empty door. The chances of you having chosen the prize is still 1/3, which means the chances you picked an empty door are 2/3. Since you get to switch doors, if the chances you picked an empty door are 2/3 then when you switch you have a 2/3 chance of winning the prize, compared to a 1/3 chance if you stay with the original door.
Hope this helps!
Yeah nice - not going to lie revision is boring and that problem was always interesting . Always got people puzzled