FEKRARAMAR

The first step is to establish the capacity of the bath when full, for this I will create a fictional unit known as bath units. Using the first tap as a reference, the flow rate is 1 bu/min. This gives the bath a capacity of 12 bu. The second tap is twice as fast, so has a flow rate of 2 bu/m.

Next we must establish the flow rate of the drain. If…[Read more]

The first step is to establish the capacity of the bath when full, for this I will create a fictional unit known as bath units. Using the first tap as a reference, the flow rate is 1 bu/min. This gives the bath a capacity of 12 bu. The second tap is twice as fast, so has a flow rate of 2 bu/m.

Next we must establish the flow rate of the drain. If…[Read more]

The first step is to establish the capacity of the bath when full, for this I will create a fictional unit known as bath units. Using the first tap as a reference, the flow rate is 1 bath unit/min. This gives the bath a capacity of 12 bath units. The second tap is twice as fast, so has a flow rate of 2 bath units / min.

Next we must establish the…[Read more]

The first step is to establish the capacity of the bath when full, for this I will create a fictional unit known as bath units. Using the first tap as a reference, the flow rate is 1 bath unit/min. This gives the bath a capacity of 12 bath units. The second tap is twice as fast, so has a flow rate of 2 bath units / min.

Next we must establish the…[Read more]

The Open University is the only (fully) public university in the UK. It has lower tution fees than the (semi) private universities, but it’s main feature is that it is primarily a distance learning platform.

No university will accept applicants with only secondary school qualifications, they must first gain A-Level qualifications after two…[Read more]

The simulation can be run with any number of doors, I provided the results when there are 3 doors also. Read my response more carefully, lol.

The typical definition of the Monte Hall problem is that all doors except one (excluding the door previously chosen) are opened.

Why do you say that?

When the alternate door is offered, 98 of the 99 goat doors are removed from the selection.

The original choice has 1/100 (1%) chance of being the car, therefore the one remaining door must have a 99/100 (99%) chance of being the car.

Read what I wrote again

Read what I wrote gain

A quick search shows that Cambridge offers a masters in ‘film studies’, this isn’t something that is limited only to ex-polytechnics.

I did my bachelors degree with Open University, which in practice doesn’t have any entry requirements at all. It was still a fairly comprehnsive and challenging course however.

Running the simulation with 3 doors staying with the initial door gives ~33% chance of winning, switiching doors gives a ~77% chance of winning.

If you run the simulation with 100 doors  instead, staying with the initial door gives ~1% chance of winning, switiching doors gives a ~99% chance of winning.

Running the simulation with 3 doors gives ~33% chance of winning, switiching doors gives a ~77% chance of winning.

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

I made a slight mistake in the progam, where if you initially select the car, it can give you the same door you selected as the option to swap to. I haved fixed it here :

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 <=…[Read more]

I made a slight mistake in the progam, which shouldn’t effect the probabilities much, but I haved fixed it here :

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…[Read more]

I made a slight mistake in the progam, which shouldn’t effect the probabilities much, but I haved fixed it here :

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…[Read more]

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…[Read more]

Turns out I was wrong, I wrote a simulation and it does improve your probablity of winning.

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 =…[Read more]

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.…[Read more]

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…[Read more]