simple vocabulary and often used : happen

I often see this word "happen" in the article but frankly speeking I am not totally understand how to use it correctly. Today I was trying to figut it out. My studying today as follows:

Happen is only a INTRANSITIVE verb. Its is crucial that you must know it is an INTRANSITIVE. Knowing it can avoid grammer mistake. For example , we know that there is no object following the intransitive. so , if you know the word "happen" is an intransitive, you won't add an object following the word "happen" except this word " to". The explanation as follows:

 the "to" should follow the word "happend"  to express

1) do something by chance: to do something by chance and without a previous plan". Chiness means "碰巧"

 For example1 : If you happen to see him, give him these keys.

2)  occur by chance: to occur or exist by chance

For example1 : It happened to be the last one in the store.

                      The trading happened to get executed. (Complete: The trading system had a problem on that day and the trading happened to get executed.