In a small village, Keiji, Nia, and Olumide were preparing for a surprise birthday party for their friend, Priya. Keiji baked a cake and left it on his kitchen table to cool. He then went to the market to get some decorations. While he was away, Nia came to Keiji's house to drop off a gift for Priya, saw the cake, but mistakenly thought it was for Olumide's birthday, which was also coming soon. Without touching the cake, she left and later mentioned to Olumide that Keiji had prepared a surprise for him. Olumide, aware that his birthday was after Priya's, assumed Nia was mistaken and decided to not discuss it further to avoid potential confusion. The next day at Priya's surprise party, after seeing the cake, Nia realized her mistake but kept quiet not to spoil the surprise. Priya, however, saw the look of realization on Nia's face and the previous conversation between Nia and Olumide. After the party, Priya asks you if Nia knew the cake was for her all along. How do you answer based on the Theory of Mind?

Provide a brief response.
Nia did not know the cake was for Priya until she saw it at Priya's surprise party. Initially, when Nia saw the cake on Keiji's kitchen table, she incorrectly assumed it was for Olumide's upcoming birthday and even mentioned this to Olumide, which indicates that at that time, she did not understand the cake's true purpose. Olumide guessed that Nia had been mistaken since he knew that Priya's birthday was to be celebrated before his, but he chose not to correct her then, to keep from complicating matters. Only during the party when Nia saw the cake being presented to Priya did she realize that her assumption was incorrect. Therefore, it was not until the party that Nia became aware that the cake was meant for Priya. Priya, interpreting Nia's realization, might have been unsure whether Nia had known the cake was for her. However, the sequence of events indicates Nia's knowledge of the cake's intended recipient only came to light during the actual celebration.