Optimization of Probability or Strategy

The question asks to determine a choice or strategy that maximizes or minimizes a probability of a specified outcome.

turkey-yks 2013 Q22 View
A bag contains nine balls numbered from 1 to 9. Ayşe will choose a number from 1 to 9 and then draw a ball randomly from the bag. Ayşe wins the game if the sum of the number on the ball and the number she chose is at most 9 and their product is at least 9.
Which number should Ayşe choose so that her probability of winning the game is highest?
A) 2
B) 3
C) 4
D) 5
E) 6