Tree diagrams
Tree diagrams are a visual way of showing all possible outcomes of two or more events. Each branch is a possible outcome and is labelled with a probability.
Two events are independent if the probability of the first event happening has no impact on the probability of the second event happening.
For example, the probability of rolling a 6 on a dice will not affect the probability of rolling a 6 the next time. The scores on the dice are independent.
If a dice was to be rolled twice, the tree diagram would look like this:
There are four possible outcomes. To work out the probabilities of each total outcome, multiply the probabilities together.
Question
A bag contains 4 blue counters and 3 red counters. A box contains 5 blue counters and 2 red counters. Complete the tree diagram and work out the probability of selecting two red counters.
Use the fact that probabilities add up to 1 to work out the probabilities of the missing branches.
The probability of selecting two red counters is \(\frac{3}{7} \times \frac{2}{7} = \frac{6}{49}\).
Question
A bag contains 10 red counters and 6 blue counters. Two counters are taken out and they are both different colours. What is the probability that the next counter taken out is red?
The probability of taking out a red counter next is \(\frac{9}{14}\).
