Basic IQ / Maths question

TheNorfolkMafia wrote:

Needless to say, the only person likely to be able to answer is possibly drac

TheNorfolkMafia wrote:

I’m in a fairly heated debate with someone on a football forum over probability and it’s an old age argument you may have encountered. To summarise , there are three doors, one has a car behind it and two have goats. The contestant picks one door and the host picks a door with a goat behind it leaving the door the contestant has picked and one more door. The host then offers the contestant the option of switching. My argument is it is now a 50/50 chance of having a car or a goat and switching doors is irrelevant but common opinion amongst PHD maths graduates is theprobability benefit of switching increasing the chance of getting to the car to 2/3 … how so?

Switching doors doesn’t statistically improve your chances of winning the car, the Monty Hall problem is a good example of how raw probabilities can be misleading.

The easiest way to demonstrate this would be to write two computer programs that randomly select doors. The first program always switches doors, the other will always keep it’s door. On average across many attempts each program will win roughly the same number of times.

This isn’t a difficult task, and I could write this for you if you wanted.

Turns out I recalled the solution inncorectly. I wrote a simulation to test the problem, swapping doors idoes mprove your chances of winnining.

Copy the following text into https://www.compilejava.net/ to run the program in your browser

import java.util.Random;

public class MontyHall
{
public static float calculateProbability(int doors, boolean swap)
{
Random rand = new Random();
int repeats = 1000;

int wins = 0;
for(int i = 0; i <= repeats; i++) {
// Place the car behind a random door
int car = rand.nextInt(doors);

// Chose a random door
int choice = rand.nextInt(doors);

// Provide an alternate door at random
int option;
if(choice == car) {
option = rand.nextInt(doors);
}else {
option = car;
}

// Swap doors
if(swap) choice = option;

// Check if the chosen door wins
if(choice == car) ++wins;
}

return ((float) wins / (float) repeats) * 100.f;
}

public static void main(String[] args)
{
int doors = 3;
System.out.println(“Simulating the Monty Hall problem with ” + doors + ” doors”);
System.out.println(“Probability of winning when not swapping is ” + calculateProbability(doors, false) + “%”);
System.out.println(“Probability of winning when swapping is ” + calculateProbability(doors, true) + “%”);
}
}

draculina wrote:

Turns out I recalled the solution inncorectly. I wrote a simulation to test the problem, swapping doors idoes mprove your chances of winnining.

This is why you shouldn’t rely on memory, and analyse things properly every time.