The correct answer for this question is option 3, Annie Besant. The Theosophical Society was indeed led by Annie Besant. It is important to note that the other options provided are incorrect.
Option 1, A. O. Hume, was not the leader of the Theosophical Society. A. O. Hume was a British civil servant in India and a co-founder of the Indian National Congress, but he was not associated with the Theosophical Society.
Option 2, Arthur Griffith, was an Irish politician and the founder of Sinn Féin, a political party in Ireland. He was not affiliated with the Theosophical Society either.
Option 4, Lord Dufferin, was a British diplomat who served as the Viceroy of India from 1884 to 1888. While Lord Dufferin had a significant role in shaping British policy in India during his tenure, he did not lead the Theosophical Society.
Therefore, based on the options provided, the correct answer is option 3, Annie Besant. She was a prominent British socialist, women`s rights activist, and supporter of Indian self-rule who served as the President of the Theosophical Society from 1907 until her death in 1933.