An interesting mental exercise

[jj]

Let us presume in port city 'A' we have a population of 1,000,000 people. Of those people, .1% have a fear of drowning in a ship accident.

Of those people, any given person with a fear of drowning in a ship accident will have a dream involving their fear and the ship docked outside their window 1/10th of the time.

One ship per day docks outside their windows.

One ship sinks every three years.

What is the chance of nobody in that town having a dream about both ships sinking?

 

[Skeptical Greg]

I think there is a pretty good chance..

Which two ships are you talking about... i.e. " both ships?

 

[Operaider]

I believe he might be refering to the discusion under the post James Randi. Half way down on the 4th page someone starts talking about 2 people that predicted the sinking of the Titanic as well as another ship.

 

[jj]

Let us presume in port city 'A' we have a population of 1,000,000 people. Of those people, .1% have a fear of drowning in a ship accident.

Of those people, any given person with a fear of drowning in a ship accident will have a dream involving their fear and the ship docked outside their window 1/10th of the time.

One ship per day docks outside their windows.

One ship sinks every three years.

What is the chance of nobody in that town having a dream about both ships sinking?

Indeed, badly phrased this is.

The last sentence should read:

What is the chance of nobody in that town having a dream about two successive ship sinkings?

 

[Just thinking]

What is the chance of nobody in that town having a dream about both ships sinking?

Both ships?

Do you mean the ship in their dream and the ship docked outside their window, or two docked ships on successive days?

Also, you do not specify over what period of time they are allowed to make the dream/sinking conection. Is it OK to have the dream on Monday and have a sinking on Thursday? Or must the sinking be within the very next 24 hour day; in other words, before they have another dream?

Anyway, let's assume 100 sinking dreams per day and 1 ship actually sinks per 1000 days (3 years is approx. 1000 days).

The probability that no one is dreaming of a sinking ship on a given day is 900 out of 1000, or 90% (0.9) to the 1000th power, or 1.75 x 10 to the -46th power. Since the chance of a ship not sinking on that day is 999/1000 (0.999), and we wish for both event to happen simultaneously, we multiply them together, and get 1.75 x 10 to the -46th power. Yes, it's basically the same number since .999 is basically 1.

But what if we wish to see if someone has a sinking ship dream on the day that one ship does sink. Then we take the 1- p value for the first value and assign 1 for the second probability (we are given that the ship does sink, hence p = 1 for that event). For the probability that someone has a sinking ship dream we get 1 - 1.75 x 10 to the -46th power, or 0.99999999999 ---- you get the picture. It's 1. Multiply that by 1 and we get --- tada 1.

In other words, it's almost certain that someone will dream of a sinking ship on the day it sinks.

 

[jj]

Re: Re: An interesting mental exercise

Originally posted by Just thinking In other words, it's almost certain that someone will dream of a sinking ship on the day it sinks.

Ayup! Precisely my point.