Fun with Probability

[Architeuthus]

I suspect that there are more than 262144 people who have flipped coins, thus an isolated series of 18 heads is not unexpected.

Like winning the lottery: not unexpected when it happens to someone else; very unexpected when it happens to you.

 

[FrumiousBandersnatch]

..You are assuming, not much of an assumption really, that the last remaining door, besides yours, had the car behind it.

Oops! Yes, I was wrong to say 'all except the car' (although it would be almost certain). I was too keen to emphasise that all the bad choices were removed, bar one (which would have a 99 in 100 chance of being good).

 

[FrumiousBandersnatch]

Well if the twist is that it is a double headed coin then that's pretty lame

That would be the most extreme case. But a coin can be weighted to fall more often on one side than another; a coin can also be tossed unfairly - e.g. flicking it up with your thumb and catching it in the same way each time will tend to give a biased sample over many trials (if you always start with the same side up).

 

[crjmurray]

Bumped for math fun.

 

[durangodawood]

That was a good brain teaser. I wouldn't have thought it really made any difference, but as suggested I read up on the Monty Hall Problem, and indeed there is a statistical advantage to switching. How interesting. The image they put on WIKI that seemed to make it click for me was this one:

Not buying it. The original 2/3 grouping is arbitrary. You could just as well have grouped 1&2 into the original 2/3.

 

[crjmurray]

Not buying it. The original 2/3 grouping is arbitrary. You could just as well have grouped 1&2 into the original 2/3.

Could you elaborate on what you mean.

 

[durangodawood]

Could you elaborate on what you mean.

Draw the diagram as if doors 1&2 share the 2/3 odds grouping, while door 3 gets labelled 1/3 (this is perfectly legit). Then see what the result (at the bottom side) looks like after the reveal.

 

[crjmurray]

Draw the diagram as if doors 1&2 share the 2/3 odds grouping, while door 3 gets labelled 1/3 (this is perfectly legit). Then see what the result (at the bottom side) looks like after the reveal.

The first door is labeled 1/3 because those are the odds of being correct on the first guess. Doors 2 and 3 are labeled 2/3 because if you switch you are essentially choosing Monty's open door and the closed door.

 

[morningstar2651]

Not buying it. The original 2/3 grouping is arbitrary. You could just as well have grouped 1&2 into the original 2/3.

I think there may be a difference between not buying it and not understanding it.

How about you try it. You'll find that you win a car 1/3 of the time by keeping your original door but much more often by switching.

If you need a much more easier way to imagine this, imagine that there are 100 doors.

You pick one door, and the host opens 98 other doors leaving you with the option to keep your original door (1% chance of having the car) or switching doors (99% chance of having the car). If you switch, you're almost guaranteed that you'll get the car.

 

[Nick665]

Not buying it. The original 2/3 grouping is arbitrary. You could just as well have grouped 1&2 into the original 2/3.

There you go , an actual experiment to proove that switching the door gives you 2/3 while holding to your original choice is still 1/3.

 

[durangodawood]

Ok ok. Youre right!

 

[DogmaHunter]

The odds shorten from one in three to one in two. So why switch?

The original odds was 1 in 3 for each door.

Your first choice thus was 1 in 3 of being correct.

When they open the door that you did NOT pick, those odds changed from 1 in 3 for the remaining doors to 1 in 2. But you picked your choice under the probability of 1 in 3.

Statistically, you still have only 1 in 3 chances that you originally picked the correct door.

By switching doors after the reveal, you (in principle) change your odds from 1 in 3 to 1 in 2.

It's pure statistics.
Your first decision had 1 in 3 of being correct.
By switching, your second decision becomes 1 in 2.


EDIT: after reading through the thread, I realised my post here is not that accurate (and in some ways simply wrong). I'm not that much of a math head when it comes to these kinds of things, but I do have this intuitive feeling that switching doors raises probabilities. And it starts with making the initial decision at a probability of 1 in 3 of picking the car, while having 2 in 3 of picking a goat, which changes after the first goat is revealed.

 

[DogmaHunter]

All that math and people are convinced by a cartoon goat.....

Universities should stop giving crazy lectures and just have Homer Simpson explain it with bottles of duff beer.

 

[crjmurray]

Universities should stop giving crazy lectures and just have Homer Simpson explain it with bottles of duff beer.

Apparently it would be wildly successful.