# Simple statistical generalization question

#### shunya

If 89% of goats have a parasitic infestation and Billy is a goat, does Billy have an 89% chance of having a parasitic infestation?

#### mathman

Forum Staff
Looks like a yes.

#### shunya

Looks like a yes.
Can you break that down for me. How exactly is that true?

#### mathman

Forum Staff
Probability equals average,

#### shunya

Probability equals average,
What does that mean?

1. 89% of goats have a parasitic infestation.

2. Billy is a goat

Therefore,

3. Billy has 89% probability of having a parasitic infestation

Is this frequentist probability?

It seems very similar to saying if 60% of 65 year olds die of a heart attack then, if you're 65 years old, you have a 60% probability of dying of a heart attack.

#### mathman

Forum Staff
Why do think there is a problem - your discussion is correct.

#### shunya

Why do think there is a problem - your discussion is correct.
I understand it now. It's the relative frequency type of probability used by insurance companies etc.

Take a representative sample, say 100 individuals, of 99 year olds and wait 5 years. If 6 of them die, the relative frequency of death in 99 year olds over a period of 5 years is 6/100 = 6%.

That means any 99 year old now has a 6% probability of dying in the coming 5 years.

#### Ludovico01

I understand it now. It's the relative frequency type of probability used by insurance companies etc.

Take a representative sample, say 100 individuals, of 99 year olds and wait 5 years. If 6 of them die, the relative frequency of death in 99 year olds over a period of 5 years is 6/100 = 6%.

That means any 99 year old now has a 6% probability of dying in the coming 5 years.
Well, I don't think that only 6/100 99 year olds would die after 5 years in reality, but if you only consider this closed system yes.

Btw I'd say that when you are talking about this kind of statistics you should also consider the life expectancy and stuff like that too