Assignment 19179

A box contains a total of five balls. The balls are numbered so they are distinct. Two of the balls are colored red and three of the balls are colored blue. The red balls are numbered 1 and 2, while the blue balls are numbered 3, 4, and 5. 2 balls are selected at random from the box. The order in which the balls are chosen does not matter but the numbers on the balls does matter. The diagram below shows three possible outcomes from the experiment. The outcome on the left and the outcome in the middle are considered the same. The outcome on the right is different than the other two. What is the expected number of red balls chosen?