Is it really 50/50 ?

[rouletteKEY]

I just saw this Monty Hall Problem on the net and it intrigued me...so I searched to see if it had been covered here before...

Here's the explanation from business insider as to why you should always switch

link:://:.businessinsider.com/the-monty-hall-math-problem-2014-2

[RouletteKnight]

Great response by everybody. This is definitely a Monty Hall problem,
though Twisteruk phrased it wrongly because someone else has to open the other boxes for you.

100 boxes may be too much for people to comprehend but lets say we use 3 boxes to understand it better.
2 of the boxes has red balls, 1 has black. You randomly choose one at the start and someone else opens another box and
reveals a red ball.  Will switching increase the odds of getting the black ball? The instinctive response will be no as there are only 2
boxes left and will be 50/50. However, this situation is different, lets take a look at how the scenario will play out...

Box 1: Black Ball
Box 2: Red Ball
Box 3: Red Ball

1st scenario: You choose box 1, someone elses open either box 2/3, switching loses
2nd scenario: You choose box 2, someone else opens box 3, switching wins
3rd scenario: You choose box 3, someone else opens box 2, switching wins.

Thus, switching actually increases the odds of getting the black ball as above.