# Learn English – Which is correct between the number of and the numbers of

grammatical-number

I am making presentation material about mathematical.

The numbers of events occurred in each sub-interval are independent.

or

The number of events occurred in each sub-interval are independent.

Which is correct? Thank you for reading my question. 🙂

X = the number of event occurred in 0s ~ 10s.

Y = the number of event occurred in 10s ~ 13s.

Z = the number of event occurred in 13s ~ 20s.

I want to say "X, Y and Z are stochastically independent".

How can I write the sentence above?

Since you refer to each (singular) sub-interval, number should also be singular. Assuming that an independent number makes sense in your field of study, you could say:

The number of events occurring in each sub-interval is independent.

If the word independent requires two arguments (X is independent of Y), you could say:

In each sub-interval, the number of events occurring is independent of that of any other sub-interval.

It may be better to use multiple but simpler sentences to express your final sample sentence:

Let X_i be the number of events occuring in sub-interval i. Then the X_i are stochastically independent.