The Monty Hall Paradox

A probability question the answer to which may seem paradoxical.

( Aside: I now have two YouTube channels. This one will be primarily for intellectual/mathematical pursuits and response videos to other YouTubers, the other channel, http://www.youtube.com/profile?user=NathanaeLman will be about the "behind the scenes" me--and will include whatever I feel like talking about, boring or interesting, mathematical or not, whether anyone's watching or not. )

Category:

Entertainment

Tags:

• nate
• math
• mathematics
• guy
• paradox
• probability
• monty
• hall
• let's
• make
• deal
• marilyn
• vos
• savant

[robakerson]

thats a lot of keys for one car

[GentleSavage1]

what I still don't get is how youtube decides when to display a comment linked as reply to someone else, and when not.

I pretty much ALWAYS click on the "reply" tag of somebody, but ery often my comment ends up being all on the top of the page. WTF?

[NavySealO3]

Simple, you have a greater chance of picking nothing, so, when he shows you nothing, if you switch, you automatically win, only if you switch.

[kirkbocek]

If you're still stuck on 50/50 as an answer to the Monty Hall Problem, check out my video response "Proving the Monty Hall Problem."

[MistyGothis]

This has been probably been mentioned before, but there are a couple assumptions you need to make about the game to justify your reasoning.

(1) The host is equally likely to hide the prize behind any of the three cups

(2) If you choose the cup with the prize, so that the remaining two cups are empty, the host is equally likely to uncover either of the two remaining cups.

[RomanNumural9]

@Drumzepplin the problem with that is 1/3 he is removing an equal amount to the amount the person chose, scale it up to your scnario you pick 33 doors and the host removes 33 doors. Ends in the same diff its like removing 2 cups and forcing the player to pick the right 1 your description that is

[xyaqua]

I love all the math and calculus they show in the background. this incredibly hard problem that humiliated PhDs and University heads, takes only a few minutes to simulate on a spreadsheet to prove that switching is correct. But the WHY, takes something that evidently a $100,000 education cannot provide- examining your preconceptions and how they can be wrong. the key- "Monte" always shows you a WRONG ANSWER, never a random pick. This is predetermined selection, and thus negates randomness

[drumzeppelin]

@TheMathGuy They would win alot more than twice as often in this scenario... if you have 100 doors, pick one, remove 98, then by switching you increase your probability to 99/100.

[phispire]

This and the Bertrand's Box problem illustrate common logical fallacies...and you guys do a great job of explaining...but there's absolutely no paradox in either problem...

[maxum905]

This paradox will only work if the host knows he is revealing a door with nothing behind it. If the host were to choose to reveal a door at random then there will be no difference in probibility between switching or not.

[cunnidvd]

Not a paradox. In the initial choice you have a 1/3 chance of being right, 2/3 of being wrong. Monty will never reveal the prize and he won't reveal your door. When you are right he has two choices. When you are wrong he has one choice with the remaing door being the prize. Since you are wrong 2/3 of the time by always switching you will be right 2/3 of the time.

[StoneOakvalley]

Uhh. I chose the first cup and stuck to it.