Why did the Federalist agree to add a bill of rights to the Constitution?

A compromise was reached on the issue of a bill of rights. The Federalists made this compromise to get enough support for the Constitution so that is would be ratified. They agreed that when the first Congress was held, it would draft a bill or rights.
The argument to add a bill of rights was  a victory for the Anti-Federalists. IT was an important addition to the Constitution and has been a of great importance in the protection of the basic rights of the American people.

Why did the Anti-Federalist want a bill of rights?

Anti-Federalist
The Constitution does not include a bill of rights. A bill of tights is necessary to protect people against the power of the national government. There is no mention of freedom of of religion, speech, press, or assembly. Since these freedoms are not in the Constitution, government is free to violate them. Americans recently fought  a war to secure their fundamental rights. They do not want a constitution that places those rights in jeopardy.
Federalist
A bill of rights is not needed. The Constitution is the ultimate protection for the people's rights and the people are the ultimate sovereigns. The Constitution does not give government the power to deprive people of their rights. It gives government only limited power to do certain things. A bill of rights will give the impression that the people can expect protection only for the rights that are actually listed.The Constitution protects a number of tights by requiring writs of habeas corpus, and prohibiting ex post facto laws and bill of attainder.