What is the probability that human beings come to know the purpose for their birth before they die?

Depends how deep they are willing to look. The more you have reincarnated the more likely you’ll remember. The earths realm has a lot of distractions that will steer one away though.

The probability increases with a strong desire to know the purpose, plus the ability to discern and think and question everything that one knows to be true. To find out is more important than to follow, but following books or what others say is easier so we rarely try to find out our purpose with our own mind.
Every human being has a different purpose, we ourselves give meaning to our life by creating a purpose. Do we need a purpose?
As @Greenbare said, the purpose of life and existence in general is existence itself, to live.
The probablity depends on how much one is willing to go beyond levels of mind and society to know the purpose, without any expectations.

Our purpose is to procreate