Hi Svetlana...

We use a word pretty common here in the United States.

Blurt

She blurted something out.

He blurted that out?

Why did you blurt that out?

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"to make a random guess."  Wouldn't be something that related to blurting something that.

For example, we could say something like, "How many balls do you think are in this box, take a random guess."

You would try to guess how many you think are in there, a "random number."  You could answer something like that with, "I think 155 balls are in there."

If you are looking for an idiom particularly, I think "Spur of the moment" comes close to your intended meaning. 

Ex - Was it a spur of the moment talk?  

Also,

Is your India trip a spur of the moment kind of adventure?

There are many phrases for different kinds of spontaneous speech.

One is "to babble." When I realize I've been speaking randomly for two long I'll apologize and say "I'm sorry, I guess I've just been babbling on."

To me, "to blurt" means to say accidentally say something that you didn't mean to say--something true but embarrassing to yourself or unflattering or hurtful to someone else. 

"To speak extemporaneously" means to give a good, clear, coherent speech without having prepared or planned it.