Two jars, J1 J_1\,J1 and J2J_2J2, contain blue, white, and black marbles. Jar J1 J_1\,J1 contains 4 blue marbles, 3 white marbles, and 3 black marbles. Jar J2 J_2\,J2 contains 2 blue marbles, 5 white marbles, and 1 black marble. Sam picks one marble at random from jar J1 J_1\,J1 and places it into jar J2J_2J2. Sam then picks one marble at random from jar J2J_2J2.
Draw a tree diagram to represent this information.
Find the probability that Sam picks two marbles of the same colour.
Given that both marbles are the same colour, find the probability they are both black.
