Suppose two groups independently implement the Bitcoin protocol. Some miners run implementation A and other miners run implementation B$.$ At some point an attacker finds a vulnerability in implementation A that causes miners running that implementation to accept transactions that double spend a UTXO. Implementation B treats such transactions as invalid.

a$)$ Suppose $80\%$ of the mining power runs the buggy implementation and $20\%$ runs the non$-$buggy one. What will happen to the blockchain once a block containing a double$-$spending transaction is submitted to the network?

b$)$ What will happen to the blockchain in the reverse situation where $20\%$ of the mining power runs the buggy implementation and $80\%$ runs the non$-$buggy one? That is$,$ what will happen to the blockchain once a block containing a double$-$spending transaction is submitted to the network?Alice is on a backpacking trip and is worried about her devices containing private keys getting stolen. She wants to store her bitcoins in such a way that they can be redeemed via knowledge of a password P$.$ Accordingly, she stores them in the following ScriptPubKey address: