In the Monty thing.
IF you choose the door Monty opened, then changing your choice to one of the remaining doors gives you a 50/50 chance of winning. If you had choosen one of the other doors to begin with, then changing your choice has no effect on the odds at all.
Your chances were 50/50 from the very start. There is no difference between a 1 in 3 chance where one is removed (and you are then free to choose between the remaining two) or one where you just choose from two to begin with.
If the original had been, you choose one of three, if your first guess is wrong then you can choose again, then your odds are really 2 in 3. Taken from the start. But calculated this way.
Original chance of getting it right roughly 33% (1 in 3)
second change 50% (1 in 2)
Your chance of winning is 88%
Wait a minute, got that wrong.
Your chance of losing the first round is roughly 66%
Your chance of losing the second round is then 50 percent. (or 33% of the original chance)
so your chance of winning at the outset is 66% 33% from the first and 33 more percent of the remaining original.
I explained it wrong but the 66% chance of winning is correct.
IF you choose the door Monty opened, then changing your choice to one of the remaining doors gives you a 50/50 chance of winning. If you had choosen one of the other doors to begin with, then changing your choice has no effect on the odds at all.
Your chances were 50/50 from the very start. There is no difference between a 1 in 3 chance where one is removed (and you are then free to choose between the remaining two) or one where you just choose from two to begin with.
If the original had been, you choose one of three, if your first guess is wrong then you can choose again, then your odds are really 2 in 3. Taken from the start. But calculated this way.
Original chance of getting it right roughly 33% (1 in 3)
second change 50% (1 in 2)
Your chance of winning is 88%
Wait a minute, got that wrong.
Your chance of losing the first round is roughly 66%
Your chance of losing the second round is then 50 percent. (or 33% of the original chance)
so your chance of winning at the outset is 66% 33% from the first and 33 more percent of the remaining original.
I explained it wrong but the 66% chance of winning is correct.