It is true that God our Father knew that when he placed Adam and Eve on this earth that they would fall. For this reason he called and ordained a Savior before the foundations of this earth.
1 Peter 1:19-20
19 But with the precious blood of Christ, as of a lamb without blemish and without spot:
20 Who verily was foreordained before the foundation of the world, but was manifest in these last times for you,
So why would God put us on this earth to fall? If God knew in advance that Adam and Eve would fall, why did he place them in garden? To understand the true reason, one needs to understand the true nature of God.
John 17:3
3 And this is life eternal, that they might know thee the only true God, and Jesus Christ, whom thou hast sent.
The key to understanding this is to know that God is not an ex nihilo creator. Ex Nihilo creation is a false doctrine that is never taught in the Bible. It has come about from the philosophies of men over a long time but was never part of the gospel of Jesus Christ. We used to believe in Newton's law of the conservation of matter. It is true that matter is eternal in nature. It is also true that God is a self existent being. What is not understood by many who profess to be Christian is that mankind also exists upon the same principle. There is a part of man's spirit that is as self existent as God himself. There was never a time when that part of man which thinks and chooses did not exist. We are eternal beings by nature.
God took of that eternal part of man that thinks and chooses and created a spirit body from spirit matter. When we came to this earth, God created Adam and Eve from the dust of this earth and put into man his spirit. Creation is not to create out nothing but to create out things that already exist.
We say that God is all powerful. What does that mean? Can God create a rock so heavy he can't lift it? Can God be all good and all evil simultaneously? Can God create something that is Self Existent out of nothing? I suggest to you that God is all powerful in that he can do all things that are possible. We, in our imperfect state, do not fully comprehend all that is possible. But God does. He can anything that is possible. But there are eternal impossibilities. God did not create himself out of nothing. That is an eternal impossibility. God could not create anything else that is self existent either. That too would be an eternal impossibility. If that part of man that thinks and chooses is eternal by nature, then God could not have created man from nothing. He may have formed man's spirit body from spirit matter and formed our physical bodies from the dust of the earth, but that eternal part of man that has always existed was not created or made and neither indeed can be.
If God could not create that part of man that thinks and chooses, then he could not create it to be perfect. For this reason evil exists because man is eternal by nature and is in an imperfect state. God could not create that which is self existent. Thus God could not create us to be perfect. If one believes in ex nihilo creation, one must also believe that God could and should have created us to be perfect. But God is not an ex nihilo creator. "Man was also in the beginning with God, intelligence, or the light of truth, was not created or made and neither indeed can be"(D&C 93:29). Thus for God to help man progress, he needed to teach man correct principles and let man choose for himself.
To truly be a good person, one must have free will. Free will is critical to truly becoming a good being. If you were to force a being to be good, would he still be a good being when stop the force? Would he really be a good being while you are forcing him to be good? it is only when man chooses goodness in and of himself that he is truly a good being. True good beings do good of their own volition and not by force. God realizes this and this is why God holds free will inviolate.
So to get back to our original question, Why would God put us on this earth to fall? It was God's intention to allow mankind to learn and grow by experience. This life is a school ground for us to experience good and evil. God couldn't force us to fall for that would be wrong on God's part. So he had a plan to help us grow and progress to become better beings. He would place us in a temporary state to experience good and evil, life and death, pain and joy. He also gave us a body. He gave us a choice before the foundation of this earth to come to this earth life and progress to become more like God himself. So he placed a vale over the minds of Adam and Eve so as not to remember their pre-mortal state. He allowed them to choose for themselves what to do. He placed Satan in their midst to tempt them. And yes, he knew they would fall. By falling from heaven, they were able to experience good and evil and have knowledge of it in order to become more like God himself.
Genesis 3:22
22 And the Lord God said, Behold, the man is become as one of us, to know good and evil: and now, lest he put forth his hand, and take also of the tree of life, and eat, and live for ever:
It was God's plan that mankind fall and experience this good and evil as well as gain a body. But being in a fallen state required salvation from the fallen state. for this reason Christ was chosen to be our Savior before the foundation of the world. Through him all mankind would be resurrected whether they do good or evil. thus all mankind would be redeemed from the fall. But those who choose evil in this life will not live among those who choose good in eternity nor will they be given the blessings of those who choose good. All will receive immortality but not all will inherit eternal life.
So, yes God knew that Adam and Eve would fall, yes, he did place them in a position to fall, but God provided a means whereby they would all be redeemed from the fall through the resurrection of the dead. But according to their own choices here on earth, they would be judged whether they chose good over evil.