Tree Diagrams
Tree diagrams show a clear pattern of probabilities in branches rather than in a table; the product of the probabilities of along a branch gives the probability of the event of that branch.
The following examples show how the way they are used in two different situations.
E.g.1
There are 5 blue balls and 4 yellow balls in a container. A ball is taken out at random, colour noted and put back in. A second ball is taken out, and the procedure is repeated. Calculate the probability of
getting two balls of different colours.
P(B,Y) = 5/9 X 4/9 = 20 / 81
P(Y,B) = 4/9 X 5/9 = 20 /81
Since events (B,Y) and (Y,B) cannot happen at the same time, they are mutually exclusive. Therefore, 'OR' rule can be applied.
P(Balls of different colours) = 20/81 + 20/81 = 40/81
E.g.2
There are 5 blue balls and 4 yellow balls in a container. A ball is taken out at random, colour noted and not put back in. A second ball is taken out, and the procedure is repeated. Calculate the probability of
getting two balls of different colours and two blue balls.
On the second draw, the total number of balls has gone down by one and so has the number of the balls in the previous draw.
P(B,Y) = 5/9 X 4/8 = 20 /72
P(Y,B) = 4/9 X 5/8 = 20 /72
Since events (B,Y) and (Y,B) cannot happen at the same time, they are mutually exclusive. Therefore, 'OR' rule can be applied.
P(Balls of different colours) = 20/72 + 20/72 = 40/72 = 5/9
P(B,B) = 5/9 X 4/8 = 20 /72 = 5/9