He's sure that Juliet will accept his plan because Juliet has just vowed that she would rather kill herself than have to marry Paris and he is offering her a way to get out of marrying Paris that isn't as scary as killing herself.
Juliet and Friar Lawrence made the plan to fake Juliet's death so she could runaway with Romeo. They had planed for her to take a vile that would make her cold and fall asleep for 48 hours. Friar Lawrence sent a note to Romeo telling of their plan so Romeo and Friar Lawrence could go retrieve Juliet once her funeral was over.
Juliet threat to kill her self
Friar Lawrence's plan went wrong when the message he sent to Romeo informing him of Juliet's fake death did not reach him in time. This miscommunication led to Romeo believing Juliet was truly dead, causing him to take his own life. Ultimately, Friar Lawrence's plan failed due to poor timing and unforeseen circumstances.
She is confused and desperate because she does not know what to do and was going to kill herself if Friar Lawrence did not come up with a plan to help her.
She was anxious and desperate. If the Friar had not thought of a plan her intent was to kill herself, right there.
Juliet was scared of Friar Lawrence's plan because she was afraid it might not work and she would be forced to marry Paris against her will. She also feared the consequences of faking her own death, such as waking up alone in the tomb or being buried alive.
Friar Lawrence organises for Friar John to bring Romeo news of Friar Lawrence and Juliets plan (Act Five, Scene 1)
Juliet meets Friar Lawrence at his cell, where they form a plan to fake her death using a potion that will make her appear lifeless. She hopes to avoid marrying Paris and reunite with Romeo.
Friar Lawrence's plan to fake Juliet's death involved giving her a sleeping potion that would make her appear dead. The consequences of this plan were tragic, as it led to misunderstandings, miscommunication, and ultimately the deaths of Romeo and Juliet. Friar Lawrence's well-intentioned but flawed plan ended in the loss of young lives.
Romeo's advisor is Friar Lawrence and Juliet's is the nurse. However, when the nurse counsels her to commit bigamy, she goes to Friar Lawrence for help. The friar proves to be a broken reed, taking inadequate steps to advise Romeo of his plan and abandoning Juliet in the tomb which allows her to commit suicide.
Friar Lawrence is concerned for Romeo's well-being and advises him to accept the consequences of the prince's decree. He tries to comfort Romeo by reminding him that banishment is a more merciful punishment than death, but also warns him to be cautious. The decree ultimately puts pressure on Friar Lawrence to come up with a plan to reunite Romeo and Juliet.
Friar Lawrence's plan at the end of Act 3, Scene 3 in "Romeo and Juliet" is for Romeo to spend the night with Juliet and then leave for Mantua in the morning. The Friar hopes this will allow Romeo and Juliet to eventually be reunited and that their marriage will bring an end to the feud between the Capulets and Montagues.