Understanding Maths: Tree Diagrams Simplified

Tree Diagrams for Consecutive Events

Ever wondered how to calculate the chances of it raining two days in a row? Tree diagrams make these tricky probability problems much easier to solve.

When you're dealing with two events happening consecutively, tree diagrams help you map out all possible outcomes. You multiply probabilities along each branch to find the chance of that specific sequence happening. Remember, if P(rain) = 1/5, then P(no rain) = 4/5 since probabilities must add up to 1.

For the rain example, you get four possible outcomes: rain-rain $1/25$, rain-no rain $4/25$, no rain-rain $4/25$, and no rain-no rain $16/25$. To find the probability of rain on exactly one day, you add the probabilities of the two ways this can happen: 4/25 + 4/25 = 8/25.

Quick tip: Always check your final probabilities add up to 1 - it's a great way to spot mistakes!

The same method works with decimals too. If Jenny's late with probability 0.3, then she's on time with probability 0.7. Following the branches shows that she's never late on consecutive days with probability 0.49, and late exactly once with probability 0.42.