c4countdown

I live just outside York whose population are seen to be quite "normal". Considering this, when I leave my house tonight, what is the probability that the first person I see will have an above average number of legs for a human?

(By average I mean the usual average - i.e. mathematical mean)

Kirk

The average number of legs is a bit less than 2, given that a small number of people have no legs or only one leg, while barely anyone has more than 2 legs. So the probability that you see someone with more than the mean number (e.g. two) is, well, close to 1 I'd say.

Spot on. The mean number of legs for a human is as you said, 1.999999999999999999999999999999999999999999 ish and so the probability is more-or-less 1 (although I think statisticians would say exactly 1 but I disagree with their philosophy).

The reason I disagree with their philosophy is similar to why I disagreed with Paul Howe's argument that picking two random numbers the same occurs with probability zero. So, picking 1 and 5 occurs with probability zero. Picking 56788 and 234543322 occurs with probability zero. Adding all these combinations together should give me a probability of 1. 0+0+0+0+..... = 1. What nonsense.

I think it should be infinitesimally small, so it's 1/infinity + 1/infinity ....... infinity times and this would add up to 1. I'd imagine this is a bastardization of maths, but it's easier (for me) to understand.

Kirk, I thought a spooky but still perfectly logical problem would've been right up your street

I've actually just thought of another problem that confounds most people's expectations (at least if they haven't seen it before) and also has nothing to do with probability, which I'll post later this week. Hopefully this will be more to your taste!

Kirk Bevins wrote:(although I think statisticians would say exactly 1 but I disagree with their philosophy).

They most certainly wouldn't, unless he or she was an idiot. The number of people in the world is finite, so the probability is going to be exactly something fractionally smaller than zero.

The problem with the numbers on paper example is that infinity is involved, and if we are going to explain things properly we have to talk about limits. Let's look at it this way:

Suppose you're measuring the height of people. You'll find that with some relatively large probability, a randomly selected person's height is, to the nearest metre, 1 metre. Now let's try and measure their height to the nearest 10 centimetres, now the probability they are exactly 1.4m tall is going to be a fair bit less than their height being 1m. So now let's measure to the nearest 1 cm, again the probability gets smaller.

The point is, that as your measuring gets more and more precise, the probability of finding someone whose height is close enough to whatever height you're measuring gets smaller and smaller, and since you could go on measuring smaller and smaller distances forever, this probability tends to zero (that is to say, it is getting smaller and smaller and can never reach some lower limit other than zero).

It's a similar thing with the numbers example, the probability of picking *exactly* 5 is basically zero, but we don't sit there and talk about limits and infinity because usually that just confuses people even more.

It's not philosophy, just maths

What is the probability of seeing a blackjack table in England?

Is American Blackjack the same as 21, Vingt-et-un and Pontoon? To me Blackjack is that game where if a black jack is played the next person picks up 7 cards (unless they have red jack which cancels it)

No, Blackjack is the game where you try to get as close to 21 as possible without going over. The term, "doubling down" was popularized because of that game.

In other words yes, it's the same as pontoon.

dinos_the_chemist wrote:To me Blackjack is that game where if a black jack is played the next person picks up 7 cards (unless they have red jack which cancels it)

I love that game, especially when we play with rules where you can stack up black jacks and 2s to make a hideous penalty. And especially when I've preloaded the deck.

What do you call pontoon?

Michael, do you mean a probability fractionally larger than zero, rather than less than zero

Did someone say fractions were involved in this?

Kirk Bevins wrote:Michael, do you mean a probability fractionally larger than zero, rather than less than zero

Close..I actually meant fractionally less than 1...

(if I told you about these new fangled probabilities which are less than zero, I'd have you kill you...or something...)

Is this just a hypothetical question?

Jason, mate, what you call Blackjack we Brits call Pontoon. There's another card game called Blackjack but its more of a kids game and not played in casinos and the rules are a bit ambiguous and it seems each person I play with uses different rules.
As for the fractions, they were to do with the original post on this thread which was a riddle to do with probability (hence the title!)

I understand some British English a lot better now.

Thank you!

Kirk Bevins wrote:I live just outside York whose population are seen to be quite "normal".

Hmmmm

Ha ha - the funniest post ever.