Chapter 3-2. Monty Hall problem
Higher category : 【Statistics】 Chapter 3. Probability Space
1. Situation
2. Premise
3. Definition
6. Conclusion
1. Situation
⑴ a super car stands behind one of the three doors
⑵ a show participant choose one of the three doors
⑶ the show host opens any of the doors that the show participant did not open
⑷ the show participant can stick to or change his or her existing choice
⑸ question: which choice is reasonable?
2. Premise
⑴ the show participant chooses door #1 at first
⑵ afterward, the show host opens the door #3
3. Definition
⑴ P(ⅰ) : the probability that there’s a super car behind door #1
⑵ P(ⅱ) : the probability that there’s a super car behind door #2
⑶ P(ⅲ) : the probability that there’s a super car behind door #3
⑷ P(Ⅰ) : the probability that the show host selects door #1
⑸ P(Ⅱ) : the probability that the show host selects door #2
⑹ P(Ⅲ) : the probability that the show host selects door #3
⑺ P(ⅰ), P(ⅱ), and P(ⅲ) are priors (causes)
⑻ P(Ⅰ), P(Ⅱ), and P(Ⅲ) are posterios (results)
4. Conditional probability
⑴ P(ⅰ | Ⅲ) : the probability that if the show host chooses door #3, there’s a super car behind door #1
⑵ P(Ⅲ | ⅰ) : the probability that if there’s a super car behind door #1, the show host selects door #3
5. Bayes’ theorem
⑴ P(ⅰ | Ⅲ)
⑵ P(ⅱ | Ⅲ)
⑶ P(ⅲ | Ⅲ)
6. Conclusion
⑴ it is advantageous for the show participant to change the initial choice
Input : 2019.07.03 22:06