Why did the Jedi think that killing Count Dooku and General Grievous would end the war?

Question

In Star Wars Episode I: The Phantom Menace, Yoda demonstrates knowledge of the Rule of Two. However, in Star Wars Episode III: Revenge of the Sith, the Council seems to fully expect defeating Dooku and Grievous to result in a Republic victory of The Clone Wars. Why?

Answer 1

The Jedi don't decide when the war is or isn't over, they're just servants of the Republic. The Senate decides when the war is over, and Palpatine makes it clear that they would consider the death of Grievous a key victory condition. The Jedi obeyed their wishes.

MACE WlNDU: Chancellor Palpatine, what a welcome sight! Are you all right?

PALPATINE: Yes, thanks to your two Jedi Knights. They killed Count Dooku, but General Grievous has escaped once again.

MACE WlNDU: General Grievous will run and hide as he always does. He is a coward.

PALPATINE: That maybe true, but with Count Dooku dead, he is the leader of the Droid Army, and I assure you, the Senate will vote to continue the war as long as Grievous is alive.

MACE WlNDU: Then the Jedi Council will make finding Grievous our highest priority.

Obviously Palpatine "assuring" the Jedi that "the Senate" would vote to continue the war was his way of saying that he would make sure the war continues until Grievous is dead. Anakin makes this clear later:

BAIL ORGANA: The end of Count Dooku will surely bring an end to this war, and an end to the Chancellor's draconian security measures.

ANAKIN: I wish that were so, but the fighting is going to continue until General Grievous is spare parts... The Chancellor is very clear about that.

As for whether the Jedi should have surmised that the Sith threat was still out there, you're correct that Yoda knew about the Rule of Two. But keep in mind he said that following the death of Darth Maul. From the perspective of the Jedi, they killed one Sith, and then killed a second one. Job well done!

Answer 2

The Jedi Order was in the dark and they were blindsided by their own arrogance.

They knew there was at least one Sith, Dark Maul, running around; they did not know if it was a master or an apprentice.

So they could only turn to the 2 public figures, Dooku and Grievous.

Count Dooku was publicly against the Republic; it was an easy "target" for the Jedi to track and take down, and more so because he was an ex-jedi.

Same thing for Grievous, he was the general of the Separatists, and a easy target; Maybe they thought that by killing the general, it would stop the separatists movement.

The Jedi didn't know who was pulling the string up to the last moment.