MSJC85

I don’t really understand why people are so obsessed about tuition fees in the UK. Nobody ever pays back much of their loan, so university is practically free.

For people who are not familiar with the system, I will explain how the UK system works currently. Firstly student loans aren’t actually loans, they don’t affect your credit rating or…[Read more]

It confused me at first too. I had looked at the problem in the past, but I had forgotten what the correct solution was.

Writing the simulation helped me to understant why this happens when you switch door.

Right now i’m not sure how else to explain it.

But you can run the simulation by hand if you have a pack of cards. If you replace the car with the ace of spades, and the goats with the 2 of hearts and the two of diamonds. If you place all three cards face down and shuffle their positions randomly you will see that you find the ace of spades more…[Read more]

This is why I gave the number when there are 100 doors, it’s easier to understand the effect.

That is correct.

The easiest way to explain this is that there is always a 100% probability of the car being behind a closed door. Which gives a probability of any of three doors having a ~33% chance of having the car if all doors are closed. This part I assume everyone agrees with.

When the goat door is opened it’s probability of having a car…[Read more]

I replied to the thread with my calculation.

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]