# Calculate Probability of a Complementary Event from Tree Diagrams

In this worksheet, students will calculate probabilities of complementary events from tree diagrams.

Key stage:  KS 3

Curriculum topic:   Probability

Curriculum subtopic:   Calculate Theoretical Probability

Difficulty level:

#### Worksheet Overview

In this activity, we are going to use tree diagrams to solve probability questions.

Given the following tree diagram, how could we find the probability that a bus is late on both days?

We want the probability that the bus is late on Monday and on Tuesday, i.e. the probability of the green path:

Anytime we are finding the probability of something 'and' something happening or the probability on the same path on the tree diagram, we multiply the probabilities:

P(late and late) = 0.3 x 0.3 = 0.09

Now, how could we use this to find the probability that the bus will not be late on both days?

Let's remember that that the probability of something not happening is 1 minus the probability of it happening:

P(not A) = 1 - P(A)

So the probability that the bus will not be late on both days can be found by subtracting the probability that it will be late on both days from 1:

P(won't be late both days) = 1 - P(late on both) = 1 - 0.09 = 0.91

Ready to put this into practice?

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