{Assignment}

2.a. What is five plus two times six minus three? Answer: 14

2.b. What should you do? Will changing your mind affect your odds of winning the million dollars? Or should you just stick with door number three?
Answer: Eliminating door number 2 just increased my odds of winning because then there is a 50% chance that the door I chose has the million dollars. Door number 1 may have a booby prize or the million dollars, but door number 3 - the door I chose - also has that same possibility of having the booby prize or the million dollars. Since it's a 50-50 situation, choosing whichever door wouldn't really matter. I would choose door number 3 if that's what my instinct tells me, or I would choose door number 1 if I feel that it's a good move to change. For me it's really a matter of in which situation would I feel worse afterwards. Would I feel worse that I lost knowing I stuck by a wrong decision the whole time, or would I feel worse knowing that I had the right decision and then I changed it the last minute? Personally, the latter would probably feel worse.

P.S. After answering I was very intrigued and looked up this paradox. And I was wrong. I knew something had to be wrong. You wouldn't give it as an example or wouldn't even bother to warn us about thinking hard about this one, if it were that simple and obvious. And so I read that this is an example of conditional probability. I didn't get a high grade in my Statistics class back in college so no wonder I did not get this one. It took time for me to understand it and below is the simplest way I can explain it.

Facts:
Let's say that Door 1 - is the $1 million, Door 2 - is the duck, Door 3 - is another duck.
The host will ALWAYS show me ONE wrong door (either Door 2 or Door 3) after I've made my first decision.
Goal:
The question here is do I STAY with my original decision or do I CHANGE it - which of the two has a higher probability for success?

TO STAY A:
I choose Door 1, Host shows me incorrect Door 2 (or 3) so I THINK I have 50-50 chance so I decide to stay - and I win.
TO STAY B:
I choose Door 2, Host shows me incorrect Door 3 so I THINK I have 50-50 chance so I decide to stay - and I lose.
TO STAY C:
I choose Door 3, Host shows me incorrect Door 2 so I THINK I have 50-50 chance so I decide to stay - and I lose.
*STAYING thus has a 1/3 probability for success.

TO CHANGE A:
I choose Door 1, Host shows me incorrect Door 2 (or 3) so I THINK I have 50-50 chance so I decide to change - and I lose (whichever the case because Door 2 and 3 are both incorrect).
TO CHANGE B:
I choose Door 2, Host shows me incorrect Door 3 so I THINK I have 50-50 chance so I decide to change to Door 1 - and I win.
TO CHANGE C:
I choose Door 3, Host shows me incorrect Door 2 so I THINK I have 50-50 chance so I decide to change to Door 1 - and I win.
*CHANGING thus has 2/3 probability of success.