Probability Tree Diagrams (Cambridge (CIE) IGCSE Maths)

• When multiplying along branches with fractions, don't cancel fractions in your working - having the same denominator makes them easier to add together!

A worker drives through two sets of traffic lights on their way to work.
Each set of traffic lights has only two options: green or red.
The probability of the first set of traffic lights being on green is .
The probability of the second set of traffic lights being on green is .

(a) Draw and label a tree diagram. Show the probabilities of every possible outcome.

Work out the probabilities of each set of traffic lights being on red, R
Use P(red) = 1 - P(green)

Draw the branches (with a label of G or R on the ends)
Write the probabilities above each branch
Calculate probabilities of each outcome by multiplying along the branches from left to right

 (b) Find the probability that both sets of traffic lights are on red.

This is the answer for P(R, R) from the tree diagram

(c) Find the probability that at least one set of traffic lights are on red.

This means the 1st is green and the 2nd is red
Or the 1st is red and the 2nd is green
Or the 1st is red and the 2nd is red ('at least one' could mean both)
Add between the separate cases

Alternative Method
At least one red means all the possible cases shown except two greens
So P(at least 1 red) = 1 - P(two greens)