Number
Number
Statistics and Probability
Algebra
Geometry and Measures
Mock Exams

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.

Tree_Dia_Q1
2. What is the probability failing followed by passing?
Using the AND rule for calculating conditional probabilities:
P(fail AND pass) = 0.3×0.6 = 0.18

3. What is the probability failing twice?
Using the AND rule for calculating conditional probabilities:
P(fail AND fail) = 0.3×0.4 = 0.12

Tree Diagrams

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

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