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Is this a valid sentence?

  1. The chances of her saying yes are high.

Gerunds always confuse me. Should I say that (if possible) or

  1. The chances that she says yes are high.
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    Per this chart, we usually use probability rather than chance in such contexts. But if we do use the latter, it's more likely to be singular form. That's for the that versions - the chance[s] of something happening is a perfectly normal construction. – FumbleFingers Reinstate Monica Oct 21 '16 at 17:36
  • @Fumble - You forgot about likelihood. Also, I don't know if we'd use probability if we were taking about, say, a marriage proposal, no matter what the ngram depicts. – J.R. Oct 21 '16 at 21:25
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The sentence:

The chances of her saying yes are high.

is fine in normal speech. Presumably in a situation such as:

I asked Jenni to the Drag Races on Saturday. The chances of her saying yes are high.

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Yes, this a perfectly acceptable sentence. You can also say:

The chance of her saying yes is high

I don't know if there is any substantial difference between chances and chance, so use which sounds best to you.

There are other ways to say the same thing. As FumbleFingers mentions in his comment, you can say "the probability of .." than "the chance of"; however in my opinion we don't usually use the word probability unless we actually talk about something measurable, like the odds on a game of chance, or the statistics of a particular event.

Rather, in casual conversation you would say something is "likely" or "unlikely":

It's likely that she will say yes.

It's unlikely that he will win the election.

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That is good, standard English.

A gerund is (in simple terms) the use of a verb as a noun (with "-ing"). It is a part of toolkit of the language, to allow you to use a verb, when you cannot think of a proper noun, or when it would be complicated, pompous, etc.

In "I like eating", "eating" has to be interpreted as a noun (in theory, you could say "I like alimentation", but that would sound awkward). You could interpret "eating" as a short form for "the fact that I am eating", or something of that sort.

The possibility to use a a gerund with a complement, e.g. "saying yes" ("the fact that someone says yes"), is a nice feature of the English language.

Note that in casual conversation, someone might say: "chances are, she will say yes".

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I can imagine some people talking about a script for a show that is under review, and asking themselves questions about what a girl says in at a given point.

"Well, it may be that she says 'blue' or 'heavy', here, but it seems to me that the chances that she says 'yes' are high."

Now, if you're talking to your friend and he's describing his plan to ask a girl out, then I think "the chances of her saying 'yes' are high'" is what you'd say. (Unless they aren't.)

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