Answer to Question #303613 in Statistics and Probability for Tarurendra Kushwah

Question

Question 1

In the Monty Hall Problem described by Karl, the correct approach when confronting to the decision of changing or keeping the door is to...

Option:

never change the door to increase the probability of winning the prize.

always change the door, although the probability of wining remains the same.

always change the door to have a positive impact on the probability of winning the goat.

always change the door, which will yield better chances of winning the prize.

Answer 1

Montey Hall problem is the next situation: There is 3 doors, behind one of them a prize, behind two others are goats. You pick one door, then anchorman removes one door with goat behind it. Now you can stay on the first door you've picked, or change it to another that left. The question is whether changing the door increasing the chance of winning the prize

The answer is: always change the door, which will yield better chances of winning prize.

Brief explanation:

There is ${\frac 1 3}$ probability of picking door with the prize in the first time. Since the anchorman always removes door with goat, the after he removes one, you still have ${\frac 1 3}$ probability that prize is behind the door you picked first, then there is ${\frac 2 3}$ probability that it is behind the other one that left