2.7 Tree Diagrams

1. Students have to pass an exam to gain a certificate. The probability of passing the exam at the first attempt is 0.70. Those who fail are allowed to re-sit. The probability of passing the re-sit is 0.6. No further attempts are allowed.

Draw a tree diagram of this situation.

2. What is the probability failing followed by passing?

Using the

$$\begin{array}{lll}P(\text{failANDpass)}\hfill & =\hfill & \text{0}\text{.3}\times \text{0}\text{.6}\hfill \\ \hfill & =\hfill & 0.18\hfill \end{array}$$**AND**rule for calculating conditional probabilities:

3. What is the probability failing twice?

Using the

$$\begin{array}{lll}P(\text{failANDfail)}\hfill & =\hfill & \text{0}\text{.3}\times \text{0}\text{.4}\hfill \\ \hfill & =\hfill & 0.12\hfill \end{array}$$**AND**rule for calculating conditional probabilities:

## Tree Diagrams

The sum of the outcomes for each event must be equal to 1.