Changing composition and probability trees

Update the available objects

Without replacement, the second selection is made from one fewer object. The colour removed also changes its remaining count. Write probabilities for the situation at the start of each branch.

The tree below represents two random draws without replacement from \(5\) red and \(6\) blue counters. \(R\) means red and \(B\) means blue. The first pair of branches is the first draw; the next pair is the second draw.

The probabilities on branches leaving any one junction add to 1. Multiply along a complete path. Add only the disjoint paths that match the required event.

“Different colours” includes \(RB\) and \(BR\). Order may not matter to the event, but both ordered paths must be counted. A single product represents just one of them.