Who sang With a Little Bit of Luck in My Fair Lady and what were the circumstances?

In the musical My Fair Lady, With a Little Bit of Luck is sung by Eliza Doolittle, a Cockney flower girl. In the scene, Eliza is feeling optimistic and hopeful about her chances of becoming a proper lady. She believes that with a little bit of luck, she can achieve her goals and transform herself into the person she wants to be.