Independent Events and Probability Trees

Question

There is a bag filled with 5 blue, 6 red and 2 green marbles. 

A marble is taken at random from the bag, the colour is noted and then it is replaced. 

Another marble is taken at random. 

What is the probability of getting 2 the same colour?

Answer 1

You find the probability of getting blue, red and green separately and add those probabilities. Note that there are a total of 13 marbles and it is with replacement..

Blue ( 5/13)*( 5/13)=25/169

Red (6/13 )*( 6/13)=36/169

Green (2/13)*(2/13)=4/169

When you add them you get (25+36+4)/169= 65/169 = 5/13