Year 10 maths: get probability trees clear this May half term

With summer assessments approaching, May half term can be a useful moment for Year 10 pupils to tackle one specific maths difficulty. Probability trees are a good choice if you can draw the diagram but still feel unsure which numbers to multiply or add.

You do not need a holiday full of worksheets. Three short sessions, each focused on a different decision, can help you understand what the diagram means rather than simply remember a rule. Start with questions from the topics your teacher has confirmed for your assessment.

1. Give every branch a clear meaning

Begin with two events whose probabilities stay the same. For example, spin a fair spinner numbered 1 to 4 twice. On each spin, the probability of getting a 4 is 1/4, and the probability of not getting a 4 is 3/4.

Draw the first pair of branches and label them “4” and “not 4”. From each endpoint, draw another pair with the same labels and probabilities.

Before calculating anything, describe one complete route aloud: “A 4 on the first spin, then not a 4 on the second.” This connects the diagram to an actual outcome.

Check that the probabilities leaving each branching point add to 1. If they do not, fix the labels before moving on. In your first session, draw two trees accurately rather than rush through ten calculations.

2. Separate one route from several possible routes

Multiply probabilities along a route to find the probability of that complete outcome. For the spinner example, getting a 4 and then not a 4 has probability:

1/4 × 3/4 = 3/16.

Now consider “exactly one 4”. There are two qualifying routes: a 4 followed by not a 4, or not a 4 followed by a 4. These are separate outcomes, so add their probabilities:

3/16 + 3/16 = 6/16 = 3/8.

Write the qualifying routes in words before doing the arithmetic. This is especially useful for phrases such as “exactly one”, “both” and “at least one”.

Try finding the probability of at least one 4 by subtracting the probability of no 4s from 1. You should get 7/16. Compare this with adding the three qualifying routes.

3. Spot when the second probabilities change

In your second session, practise a question without replacement. A bag contains three red counters and two blue counters. Two counters are taken, and the first is not returned.

If the first counter is red, two red and two blue counters remain. The second probabilities are therefore 2/4 and 2/4.

If the first counter is blue, three red and one blue remain. Those probabilities are 3/4 and 1/4.

Write the remaining contents beside each branching point. Then calculate the probability of two red counters: 3/5 × 2/4 = 3/10. Explain why the second denominator is 4, not 5.

4. Use a short assessment check

For your final session, attempt three unfamiliar questions without worked examples beside you. Include one repeated independent event, one without replacement and one asking for several possible routes.

After checking your answers, name the first decision that went wrong: interpreting the wording, labelling branches, choosing routes or calculating. Correct that step, then try a similar question on another day.

Parents can ask, “What does this route represent?” without taking over the calculation. If uncertainty keeps returning, the free 2 minute quiz can help you explore one to one support with GoodGrade Tutors.