Calculate Probability of a Complementary Event from Tree Diagrams

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?