Lisa is a grandmother and widow, and she has a bank account with $$400,000$ in her name. She is adding her grown granddaughter, Sophia, as a joint owner of this account with the right of survivorship. Which of the following statements is correct about the estate planning consequences associated with Lisa$$s action?

A$.$ At Lisa$$s death, $$200,000$ will be included in her gross estate.

B$.$ At Lisa$$s death, the account will go through probate.

C$.$ When she added Sophia to the account Lisa made a gift of $$200,000$ to Sophia.

D$.$ If Sophia withdraws any money from the account, then Lisa will have made a gift to Lisa.