Monty Hall Problem and Implications Explained

Reply #7

cottoneyedjoe — Thu, 18 Apr 2024 23:09:30 GMT

Cool result with even more generalization.

Reply #6

Orange71 — Mon, 15 Apr 2024 16:19:47 GMT

Small point, but I should say on the opening sentence, n 0 and n G (not n =G) . Since n and G are positive integers, this implies G =2. (If there were not at least two goats, there would not be a game because Monty would reveal a single goat and the player would always stay put and win.

Reply #5

Orange71 — Sun, 14 Apr 2024 22:19:12 GMT

Let's generalize to Monty opens n doors, all goats of course, where n 0 , and n =G.

Then the probability is as follows:

Since P 0 and G 1 , we need to prove the following to show that the player is better off switching doors:

We can ignore denominator and just consider the numerator.

Since n 0 and P 0 , then the product nP 0, and this proves that the player is always better off switching.

Reply #4

Orange71 — Sat, 13 Apr 2024 18:09:25 GMT

Interesting one cottoneyedjoe. I'll give it a try later.

Reply #3

cottoneyedjoe — Sat, 13 Apr 2024 16:26:03 GMT

Try the generalized Monty Hall problem: P doors have prizes behind them, G doors have goats, for a total of P+G doors. Assume P 0 and G 1. You pick a door, Monty then opens a door that contains a goat (which is always possible if G 1). He offers you to switch doors after revealing a goat.

If you play the strategy of never switching, your probability of winning a prize is P/(P+G).

If you play the strategy of always switching, what is your probability of winning a prize? Bonus: Prove that

Reply #2

Orange71 — Sat, 30 Mar 2024 15:21:36 GMT

Yes, goats. I created my post from memory, which is not perfect.

Reply #1

Brock Lee — Fri, 29 Mar 2024 21:09:48 GMT

it was goats, not donkeys. supposedly, monty hall had little tells like changes in facial expression depending on whether the player had chosen the prize or a goat.

Monty Hall Problem and Implications Explained

Orange71 — Fri, 29 Mar 2024 01:56:27 GMT

The Monty Hall problem is a famous case study in the application of Probability, specifically the concept of Conditional Probability. In simple terms Conditional Probability is the probability that something will occur given the additional information that something else has occurred. If something else is known to have occurred, it may or may not affect the probability of something .

Examples of the probability of something not being affected by something else are (a) the outcome of the n-t... [ More ]