What's this rule of probability called?

[dstebbins]

Intuitively, I would like to call this the "Law of Cumulative Probabilities," but I'm not the authority who decides what to call a particular law of mathematics.

 

When an event has "1/x" chance of occurring with a particular "successful" result, and you run the event y times, then the probability of success every time is "1/(x^y)"

 

A good example of this rule of cumulative probabilities being applied in the real world is thus:

 

Suppose there's ten serial killings across the nation. On the 10th killing, a police officer - having heard of the previous nine killings - takes it upon himself to search the customer databases of nearby hotels. He then procures the same records of hotels within 50 miles of each of the previous nine killings, and runs them through a computer to see if there are any matches.

 

Lo and behold, there is a match! Turns out, this guy named Johnny Samuel Rodrigues the Third (I just made that name up, sincet his is a hypothetical example) is known to have rented nine hotel rooms, all within three miles of their corresponding murders, and all nine stays were ended on the dates the autopsies show the murder to have happened.

 

While any one of those, standing by themselves, could be handwaived as coincidence, ten in a row is going to entitle the authorities to a warrant to the man's arrest. Or at the very least, a warrant to take the man's DNA.

 

What is this law of probabilities called?

Edited June 12, 2014 by dstebbins

[Acme]

Intuitively, I would like to call this the "Law of Cumulative Probabilities," but I'm not the authority who decides what to call a particular law of mathematics.

 

When an event has "1/x" chance of occurring with a particular "successful" result, and you run the event y times, then the probability of success every time is "1/(x^y)"

...

What is this law of probabilities called?

While I wouldn't call it a law, it strikes me as a 'compound probability'. If so then your equation is incorrect.

 

Theory that the probability that two independent events will occur is equal to the probability that one independent event will occur times the probability that a second independent event will occur. For example, on a single toss of two dimes (each dime having a head and a tail), the probability that both will land on their tails is equal to .25 (.5 x .5).

Compound Probability

[imatfaal]

Acme

 

1/x * 1/x = 1/(x^2)

 

(1/x)^y = 1/(x^y)

 

the Ops equation is correct

[Acme]

Acme

 

1/x * 1/x = 1/(x^2)

 

(1/x)^y = 1/(x^y)

 

the Ops equation is correct

I sit corrected. However, isn't that only true if all denominators are x?

Was I correct to answer the question in the OP as 'compound probability'?

[imatfaal]

The chance of getting highest value on a roll of all six D&D dice is 1/4*1/6*1/8*1/10*1/12*1/20 - so no the denominator does not have to remain the same.

[Acme]

The chance of getting highest value on a roll of all six D&D dice is 1/4*1/6*1/8*1/10*1/12*1/20 - so no the denominator does not have to remain the same.

And I am correct that this is called a compound probability?

[imatfaal]

As my maths is self taught I hate to talk about rigid definitions. Sal Khan seems to call it Compound Probability of Independent Events - so that seems good enough for me

 

https://www.khanacademy.org/math/probability/independent-dependent-probability/independent_events/v/compound-probability-of-independent-events

[dstebbins]

However, isn't that only true if all denominators are x?

Well, my OP was concerning an even twhere all denominators WERE x.

 

"If an event has x chance of success, and the event occurs y times."

 

That means that it's the same event each time.

[Acme]

Well, my OP was concerning an even twhere all denominators WERE x.

 

"If an event has x chance of success, and the event occurs y times."

 

That means that it's the same event each time.

Yes well, I was clarifying a side issue. I suspect your motel example does not qualify as the same event each time. I'm happy to have answered your question.