Monty Hall Mathematical Proof

Rules of the game.

Monty hall mathematical proof. Graphical proof of the monty hall problem. At this point the probability of success i e choosing the diamond is 1 3. Unopened ifelse door b c b sum car unopened n. The gain when switching doors is given by how many times the unopened door has the car.

As expected it is about 1 3. 2 1 3. But the car is either behind the unopened door or behind a. 1 the probability that the prize is behind door 1 2 or 3 is 3 p.

A contestant chooses one of the three cups at random move one. P 3 1 suppose that the contestant chooses door number 1. The problem as stated says that monty hall deliberately shows you a door that has a goat behind it. The monty hall problem is a brain teaser in the form of a probability puzzle loosely based on the american television game show let s make a deal and named after its original host monty hall the problem was originally posed and solved in a letter by steve selvin to the american statistician in 1975.

Sum car a n. There are three inverted cups one of which hides a valuable diamond. P h mid e frac p e mid h p e p h frac p e mid h times p h p e mid h times p h p e mid text not h times p text not h. You win if the car is not behind a.

It became famous as a question from a reader s letter quoted in marilyn vos savant s ask.