How to work out the odds of improbable events

[Richard "No Leaks" Pipe]

Some of you may remember Ashley Cotter-Cairns (aka Santa Claus, formerly of Luton, now living in Canada. One thing he did before he left was to buy a number plate from the DLVC and sell it on at a profit. Yesterday, I saw that number plate for the first time on a car and yesterday happened to be Ashley's birthday. Long odds, or not?
Is the correct thinking that it is irrelevant what the event linked to Ashley was, that occurred on his birthday, and therefore simply 364/1, in that it DID happen on his birthday. Or, does one have to factor in the improbability of anything coincidental happening on his birthday.
I seem to vaguely remember Red Dwarf covering this subject or it may have been Hitchhiker's Guide - sorry to insult the fans of these progs with my ignorance.
If I had happened to see the number plate on any non-specific date, I would have simply said "heh, mate, guess what I saw today" It would have been reasonably probable that I would have seen the number plate at some time during my life. So I'm not convinced that what seemed so improbable at the time actually was.
Any mathematicians out there?

[Simon Galloway]

Not exactly a thoroughbred mathematician but here goes...:

If you look hard enough you will always find a 'co-incidence' - for this to be long odds you would have to specify what events had to occur in advance. In other words, you have "the field" running for you - whatever unlikely event happens you are pairing it with the birthday post-event.

A bit like how mediums work - " a woman will come into your life.." "or maybe a man..." If you look hard enough, it will fit.

At the dogs a while back, Trap 6 won 5 races on the trot. A friend of mine asked:"what are the chances of trap 6 winning the next race? Must be thousands to one!" He couldn't get to grips with the fact that at the start, it would have been a great accumulator to be on, but 5 legs into it, the real probability (ignoring racing ability) was 1 in 6 (i.e. 5/1) of Trap 6 winning the next race.

Did that get anywhere near answering it??


--Previous Message--

: Some of you may remember Ashley Cotter-Cairns (aka Santa Claus, formerly of
: Luton, now living in Canada. One thing he did before he left was to buy a
: number plate from the DLVC and sell it on at a profit. Yesterday, I saw that
: number plate for the first time on a car and yesterday happened to be Ashley's
: birthday. Long odds, or not?
: Is the correct thinking that it is irrelevant what the event linked to Ashley
: was, that occurred on his birthday, and therefore simply 364/1, in that it DID
: happen on his birthday. Or, does one have to factor in the improbability of
: anything coincidental happening on his birthday.
: I seem to vaguely remember Red Dwarf covering this subject or it may have been
: Hitchhiker's Guide - sorry to insult the fans of these progs with my ignorance.
: If I had happened to see the number plate on any non-specific date, I would
: have simply said "heh, mate, guess what I saw today" It would have been
: reasonably probable that I would have seen the number plate at some time during
: my life. So I'm not convinced that what seemed so improbable at the time
: actually was.
: Any mathematicians out there?
_________________
www.teammoshman.com

[Dylan]

No longer a mathematician, but I'll give it a shot.

There's no "factoring in of improbablity" required. You're as likely to see it on Sept 29th as March 29th.

Assuming this event occurs once, the prob. of it happening on Sept 29th is 1/365. The prob. of it happening on any other unspecificied date is 364/365. But the prob. of it happening on any specific day, whether its a coincidental day or not is 1/365.

So it is a long shot that you saw the license plate on the birthday, but no more unlikely than seeing it on your birthday, or my birthday or any specific day.

Dylan



--Previous Message--

: Some of you may remember Ashley Cotter-Cairns (aka Santa Claus, formerly of
: Luton, now living in Canada. One thing he did before he left was to buy a
: number plate from the DLVC and sell it on at a profit. Yesterday, I saw that
: number plate for the first time on a car and yesterday happened to be Ashley's
: birthday. Long odds, or not?
: Is the correct thinking that it is irrelevant what the event linked to Ashley
: was, that occurred on his birthday, and therefore simply 364/1, in that it DID
: happen on his birthday. Or, does one have to factor in the improbability of
: anything coincidental happening on his birthday.
: I seem to vaguely remember Red Dwarf covering this subject or it may have been
: Hitchhiker's Guide - sorry to insult the fans of these progs with my ignorance.
: If I had happened to see the number plate on any non-specific date, I would
: have simply said "heh, mate, guess what I saw today" It would have been
: reasonably probable that I would have seen the number plate at some time during
: my life. So I'm not convinced that what seemed so improbable at the time
: actually was.
: Any mathematicians out there?

Post Edited (30/9/2003, 3:26 pm)

[gareth]

There is a great book on probability which explains to some degree how to understand the likelihood of unlikely events happening, to simplify it, once the odds of an event become astronomical i.e. winning the national lottery you are almost as likely to win it twice as once, It is difficult to understand this paradox. They call it the law of large numbers. Someone somewhere will be hit by a aircraft door on his birthday whilst winning the lottery and he is a pilot, and his surname is Boeing.

[Dylan]

What does this have to do with the law of large numbers? I can't really see the link.

--Previous Message--

: There is a great book on probability which explains to some degree how to
: understand the likelihood of unlikely events happening, to simplify it, once the
: odds of an event become astronomical i.e. winning the national lottery you are
: almost as likely to win it twice as once, It is difficult to understand this
: paradox. They call it the law of large numbers. Someone somewhere will be hit
: by a aircraft door on his birthday whilst winning the lottery and he is a pilot,
: and his surname is Boeing.

[GARETH]

ME NEITHER SORRY

[PeterB]

And if you are almost likely to as win the lottery twice as to win it once, shouldn't about one in two of the winners these days be people who have won it before?


--Previous Message--

: ME NEITHER SORRY

[Richard "No Leaks" Pipe]

Not much chance of there being a bomb on the plane you fly on, even less chance of there being two bombs, SO ALWAYS CARRY A BOMB.

[Simon Galloway]

Wouldn't we need about 14 million draws before that was right?

Surely you can shorten the odds on the lottery by asking the bad beat brigade to pick 43 numbers for you - as their luck is always completely out it can only be a matter of time before your 6 numbers remaining come up trumps...

--Previous Message--

: And if you are almost likely to as win the lottery twice as to win it once,
: shouldn't about one in two of the winners these days be people who have won it
: before?
:
: --Previous Message--
:
: ME NEITHER SORRY
_________________
www.teammoshman.com

[Dylan]

The way I remember it, the law of large numbers is about probabilities converging as samples size increases.

Say the true odds of winning the lottery was 1 million to 1. The law would say, I guess, that in practice you're more likely to win it twice out of 2 million attempts than you are to win it once out of 1 million attempts.

If this is what you're getting at, it's a very different statement to: "you are almost as likely to win [the lottery] twice as once"

Dylan

--Previous Message--

: ME NEITHER SORRY

Post Edited (30/9/2003, 5:36 pm)

[Dylan]

--Previous Message--

: The way I remember it, the law of large numbers is about probabilities
: converging as samples size increases.
:
: Say the true odds of winning the lottery was 1 million to 1. The law would
: say, I guess, that in practice you're more likely to win it twice out of
: 2 million attempts than you are to win it once out of 1 million
: attempts.
:
: If this is what you're getting at, it's a very different statement to: "you
: are almost as likely to win [the lottery] twice as once"
:
: Dylan
:
: --Previous Message--
:
: ME NEITHER SORRY
:
: Post Edited (30/9/2003, 5:36 pm)

[Prince Charles]

HI Richard

You will need to factor in the following:

First of all, we're talking about his birthday on any year - so:

you will need to know the following:

1) How many cars you are going to see in your lifetime (lets say for the region - rather than the UK)

2) The average amount of cars that are in existence(lets say for that region) on a annual basis

So if on an annual basis you're seeing 1% of the cars in existence (for that area/region) then it would mean 100 x 364 would be the odds ie 36,400 to 1 that you would ever see his car on his birthday. The maths are simple, the thing that complicates it is where in proximity the guy that bought the car is to you. Obviously, if he lives in the next road along, then the region is very small and the percentage of cars that you will see for that region will be high (on an annual basis). There is another important factor, that is you are not both driving around randomly - you have set routes - so it depends whether these routes ever cross - However if it is a random event then you can just calculate it as I put it earlier.

Mark
--Previous Message--

: Some of you may remember Ashley Cotter-Cairns (aka Santa Claus, formerly of
: Luton, now living in Canada. One thing he did before he left was to buy a
: number plate from the DLVC and sell it on at a profit. Yesterday, I saw that
: number plate for the first time on a car and yesterday happened to be Ashley's
: birthday. Long odds, or not?
: Is the correct thinking that it is irrelevant what the event linked to Ashley
: was, that occurred on his birthday, and therefore simply 364/1, in that it DID
: happen on his birthday. Or, does one have to factor in the improbability of
: anything coincidental happening on his birthday.
: I seem to vaguely remember Red Dwarf covering this subject or it may have been
: Hitchhiker's Guide - sorry to insult the fans of these progs with my ignorance.
: If I had happened to see the number plate on any non-specific date, I would
: have simply said "heh, mate, guess what I saw today" It would have been
: reasonably probable that I would have seen the number plate at some time during
: my life. So I'm not convinced that what seemed so improbable at the time
: actually was.
: Any mathematicians out there?