1. ## sentence

Over a large number of trials, the probability of an event to occur is equal to the probability that it will not occur.

Over a large number of trials, the probability of an event occuring is equal to the probability that it will not occur.

2. ## Re: sentence

Over a large number of trials, the probability of an event occurring is equal to the probability that it will not occur.

(assuming there are two possible outcomes.)

3. ## Re: sentence

Over a large number of trials, the probability of event to occur is equal to the probability that it will not occur.
I can't understand why "of event to occur' is wrong?

Over a large number of trials, the probability for an event to occur is equal to the probability that it will not occur.
Over a large number of trials, the probability of an event occuring is equal to the probability that it will not occur.
Now, the two sentence mean the same?

4. ## Re: sentence

Originally Posted by puzzle
Over a large number of trials, the probability of event to occur is equal to the probability that it will not occur.
I can't understand why "of event to occur' is wrong?

Over a large number of trials, the probability for an event to occur is equal to the probability that it will not occur.
Over a large number of trials, the probability of an event occuring is equal to the probability that it will not occur.
Now, the two sentence mean the same?

Nouns can be modified by attributes in post-position. Some nouns require infinitives to be used in that function, some nouns require gerunds, some admit of both.
E.g. He had an impulse to run away.
He didn't like the idea of travelling abroad.
He had a good opportunity to make / for making a career.

Besides stand alone infinitives or gerunds in such constructions, you can also have complexes, i.e. noun/pronoun + infinitive or gerund:
e.g. for Tom to come, for him to go
Tom's coming, his going
It's a good opportunity for him to sign the contract.
I don't like the idea of his going abroad.

In your sentence you have such a complex used as an attribute for the noun 'probability': an event occurring. 'Probability' belongs to the group of nouns that require a gerund to be used as postpositional attribute.

5. ## Re: sentence

Look at your sentence this way:
Over a large number of trials of an event, the probability to occur is equal to the probability that it will not occur.

Does that sound right to you?

OR
Over a large number of trials of an event, the probability of occurring is equal to the probability that it will not occur.
'of' is a prepostion requiring a noun - here, a verbal noun - 'occurring'.

This still hold true when we recast the sentence as you had it:
Over a large number of trials, the probability of an event occurring is equal to the probability that it will not occur.
(one of the 'of's is no longer necessary)

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