Reach for the Star | GCSE Mathematics

L073: Probability trees and combined events

Objective

Use probability trees and combine event probabilities.

Calculator: Non-calculator core; calculator optional only for checking where labelled.

Visual model for Probability trees and combined events
Points route: Connect 2 · Share 2 · Apply 6 · Review 3 · Stretch 2 · Deep Challenge 3. Record your score honestly after you have checked your answer.

Recall

Retrieve the key fact or method needed for probability trees and combined events.

Core practice

Two independent events have probabilities 0.4 and 0.7. Find P(both) and P(neither).

Reasoning

Toss a biased coin with P(H)=0.7 three times. Find P(exactly two heads).

Exam-style

A probability problem is presented with two stages. Complete the representation, calculate the probability and explain any assumption.

WWW / EBI

Recall & Review: feedback and extension integration

Lesson L073: Probability trees and combined events

Objective: Use probability trees and combine event probabilities.

60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.

What Went Well (WWW)

I represented the outcomes systematically, used the correct probability rule and checked that the probabilities or frequencies were consistent.

Even Better If (EBI)

I will show the sample space, branch or set reasoning explicitly, state any dependence or condition and check totals before giving the final probability.

Stretch and deep challenge

Stretch: Two independent events have probabilities 0.4 and 0.7. Find P(both) and P(neither).

Deep challenge: Toss a biased coin with P(H)=0.7 three times. Find P(exactly two heads).