Tree Diagrams
When you need to find the probability of 2 or more events happening a tree diagram can help.
Example
Peter and Lucy were playing games. The probability of Peter winning at Chess is 0.4 and the probability of Peter winning at Trivial Pursuits is 0.7. No draws are possible. Draw a tree diagram to represent this information. Find: (a) P(Peter wins both games),
(b) P(Lucy wins at Chess and Peter wins at Trivial Pursuits) and (c) P(Peter wins 1 game and loses the other)
.
(a) P(Peter wins boths games) = 0.28
(b) P(Lucy wins chess and Peter wins trivial pursuits) = 0.42
(c) P(Peter wins 1 game) = 0.12 + 0.42 = 0.54
Nb. Make sure you give yourself plenty of space to draw a tree diagram, and consider how many branches are required before you start.
Write clearly the probability of each branch on that branch.
The sum of the probability on each pair of branches is 1.
The sum of the probabilities on the far right hand side is 1.
The above is an example where the two games are independent of each other that is the result of the chess does not affect the result of the Trivial Pursuits. This means that the probabilities on the pairs of branches for Trivial Pursuits are the same no matter who won the chess.
Example 2
There are 15 marbles inside a velvet bag. 7 marbles are red, 5 marbles are blue and 3 marbles are white. Three marble are drawn from the bag, find P(all 3 are different colours).
P(all 3 different) = P(R, B, W) + P(R,W, B) + P(B, R, W) + P(B, W, R) + P(W, R, B) + P(W, B, R)
=
This is an example of dependent or conditional probability.