Is it the real reason that Jing Ke stabbed the king of Qin, and finally Jing Ke said that the assassination failed?

No, at that time, Qin Shihuang had stabbed Jing Ke in the thigh. He had no ability to stab Qin Shihuang at all. And even if Qin Shihuang was killed, it could not stop Qin Yanyan. Jing Ke knew it very well, so he said that he wanted to make a Covenant to serve the prince. What he meant was that he wanted to make a Covenant to bind Qin Shihuang.

For Jing Ke, This agreement should be the best way.

The plan to assassinate Qin Shihuang:

The probability of Jing Ke's death is 1%

The probability of Jing Ke's death is 1%

The agreement is at least 7% to postpone Jing Ke's death

So this plan is the best. But as far as the situation was concerned, Jing Ke was no longer able to do so.