Monty Hall Problem - Numberphile
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users link it when someone is confused by the Monty Hall problem or its variants and needs an intuitive explanation of the 2/3 probability.
Recommended by 3 people across 3 different months, 2015 to 2019.
What it is
A short Numberphile video in which Lisa Goldberg, an adjunct professor of statistics at UC Berkeley, explains the Monty Hall problem and why switching doors wins two thirds of the time. It is a conversational explainer filmed by Brady Haran, with links to an extended maths version and a beginner version.
What people said
Recommends Jansen Lopez · 2015-03 · Mathematics Stack Exchange · on “A slight variant of the Monty Hall Problem.”
This is the video that made me understand the Monty Hall Problem. I want a solution to this variant near this video's concept. [this video]
Recommends Colm Bhandal · 2015-08 · Mathematics Stack Exchange · on “Heads and tails Probability question”
@Sinan this is a very common quirk of our human minds. It's a good example of how we're not really geared to reason about probability at all. I recommend you look at the Monty hall problem e.g. [this video] It confused some of the greatest mathematicians, including Erdos!
Recommends Ojasw Upadhyay · 2016-12 · Mathematics Stack Exchange · on “The Monty Hall Problem: 2 contrasting answers.”
This is not true. The probabilities of 2/3 is in the group of the doors you haven't chosen, so if one of those is a goat and you know high one then there is a 2/3 that it is there. If you want a full explanation go to: [this video]
Cites Raymond Pang · 2016-12 · Mathematics Stack Exchange · on “The Wrong Answer of Monty Hall Problem”
@barakmanos It exists in my exam paper today and I cannot take it away. I think the teacher just copies the famous problem without any changes from the Numberphile Youtube video link [this video] . Picking first door and opening second door is just an example.
Cites actinidia · 2018-01 · Mathematics Stack Exchange · on “The need for rigorous proofs in Sets”
Because we don't really know something is true until we prove it. Here's my favorite example of this: Question: Given a circle, what is the number of regions determined by n points on its perimeter? $^{[1]}$ We begin by looking at different cases, starting from when $n=2$: [LINK] The pattern seems clear, doesn’t it? The number of regions appears to be doubling every time we add an extra point. So we suspect that with $n = 5$, there will be $16$ regions. Let's check to make sure: [LINK] That was tedious to do, but clearly we're right! Okay, so for $n\geq2$, we have that the number of regions with $n$ points, $R(n)$, is given by $2^{n-1}$. Why bother looking for a rigorous proof of this when w
Cites Bram28 · 2019-10 · Mathematics Stack Exchange · on “Are computers better at guessing random numbers than humans?”
A randomly picked number is just as likely to match another randomly picked number as does a human-picked number. Thinking that a computer-picked number has a better chance of winning than does a human-picked number because of the fact that $70$ % of all wins are scored by a computer does not mean that computers are better at this, and commits the base rate neglect fallacy [LINK] . Most likely, computers winning $70$ % of the time is the simple result of $70$ % of all tickets being picked by computers. That is, $70$ % of all people chose the option of having their numbers picked by the computer random algorithm. Simply put: the random tickets won more than hand-picked tickets did simply beca