# Is it normal (correct) to calculate a probability without knowing the sample space?

Is it normal (correct) to calculate a probability without knowing the sample space?

Background:

I have finished a probability calculation $\mathbb{P}(E)$. I want to do some simulations.
Therefore, I need to count the occurrences of the event $E$, and divide it by the cardinality of the sample space.
Suddenly, I realized that I don't know how to calculate the cardinality of the sample space (I know how to count the occurrences of the event $E$).

Is this situation normal?

More background:

The probability problem is too long to post here. The interested readers are referred to MathOverflow (No. 163869).

Roughly speaking, the event $E$ denotes a pattern in a continuously coming stream (formally, in Queueing Theory). The probability $\mathbb{P}$ considers the situation in the long run. In simulations, I can count the occurrences of the pattern. But what is the reasonable way of counting the non-patterns and thus the whole sample space?

• Why are you looking for the cardinality of the sample space when you're trying to establish the probability through a relative frequency approach? – Sudarsan Dec 16 '14 at 2:26
• @Sudarsan I need to do simulations. The cardinality of the (relative) sample space is the denominator. – hengxin Dec 16 '14 at 2:29
• The probability is just the number of times the event occurs divided by the total number of times the experiment is performed right? – Sudarsan Dec 16 '14 at 2:29
• @Sudarsan Then I don't know what the experiments are. Roughly speaking, in MathOverflow (No. 163869), the event $E$ denotes a pattern in a continuously coming stream (formally, Queueing theory). I can count the occurrences of the pattern. But what is the reasonable way of counting the non-patterns and thus the whole sample space? – hengxin Dec 16 '14 at 2:38
• It is quite common to not know the sample space. However, the usual situation is that one is investigating a random variable and knows its distribution on $\mathbb R$. Then you basically do not need to know anything about the sample space. – GenericNickname Dec 16 '14 at 10:48