Combined events: two traffic lights on the way to school
Set how often each traffic light is green and use a tree diagram and an area model to find the chance of a trip with no stops.
Core concept
For independent events, multiply along the branches: P(A and B) = P(A) × P(B); P(at least one) = 1 − P(none)
Topic: Probability of combined events
On the way to school a student passes two traffic lights, A and B. Each light is green for part of the time, and the two lights work independently: what one shows does not change the other. A tree diagram lists every outcome: green or red at A, then green or red at B. To find the probability: How likely something is to happen, from 0 (impossible) to 1 (certain). All key words of a path, multiply the probabilities along its branches. The four paths cover everything, so their probabilities add up to 1, and "at least one red" is 1 − P(both green).
What you will learn
- Draw a tree diagram for two independent events.
- Use P(A and B) = P(A) × P(B) for independent events.
- Find the probability of "at least one" using 1 − P(none).
Before you start
- Probability as a number from 0 to 1 and multiplying decimals.
Materials
- A notebook to tally the lights on the way to school
Equipment
- A watch to time each light
Procedure
- Tap − or + beside each light to change how often it is green.
- Follow the tree: multiply along each path, and check the four outcomes add up to 1.
- Compare with the square: each outcome's area is its probability.
- Record two lights green half the time, two lights green 0.7 of the time, a trip with no stops more likely than not, and one where it is rare.
How this simulation is simplified
- The two lights work independently.