Who is to blame for Adam and Eve being banished from the Garden of Eden?

After reading Genesis 2 & 3 Adam and Eve have been kicked out of the Garden of Eden.  I would blame the serpent because he was the one who lied to Eve.  In the text, he asked Eve “Did god really say, “ You must not eat from any tree in the garden?”  Eve said that they are able to eat from the trees in the garden but not the tree that is in the middle and do not touch it.  The serpent told Eve “You will not surely die”.  She believed him and ate the fruit from the middle tree and also gave it to her husband Adam to eat.  God realized that they ate from the tree because when they ate the fruit their eyes opened and they knew they were naked which Adam told god.  God cursed the serpent above all of the livestock and wild animals.  God then cursed both Adam and Eve and he banished them from the Garden of Eden. In the text, God said to Adam “By the sweat of your brow you will eat your food until you return to the ground since from it you were taken; for dust you are and to dust you will return”.   I think that Eve really believed the serpent and had she realized that he was being deceitful she would not have eaten from the tree of life and the tree of the knowledge of good and evil.