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A graph (network diagram) showing all possible combinations of outcomes for randomly drawing two balls without replacement from a jar containing 7 blue and 3 red balls, made by extending lines from a single point, branching at each possibility or decision point. Each branch is labelled with its associated probabilities. Two labelled branches, corresponding to 1st ball Blue (B1) and 1st ball Red (R1), extend to the right from a single point on the left. Probabilities are labelled as B1: 7/10 and R1: 3/10. Two additional branches extend from the end of both B1 and R1, corresponding to 2nd ball Blue (B2) and 2nd ball Red (R2), such that there are four ends to the tree on the right side (labelled B2|B1, R2|B1, B2|R1, R2|R1). These four branches are labelled with the associated probability of drawing that colour ball from the nine balls that remain after the first draw, as follows: B2|B1: 6/9, R2|B1: 3/9, B2|R1: 7/9, R2|R1: 2/9. Two columns are shown to the right of the tree diagram, Outcome, and Probability, as follows: B1 and B2: 42/90 = 14/30, B1 and R2: 21/90 = 7/30, R1 and B2: 21/90 = 7 / 30, R1 and R2: 6/90 = 2/30.

Last updated August 31, 2010