• Quick retrieval from earlier learning (Permutations and combinations; Tree diagrams and Venn diagrams). Students answer on mini whiteboards.
• Show answers together and note who needs support in the main task.

1. In how many ways can 1st, 2nd, 3rd and 4th place be awarded among 5 runners? → 120Prompt: Order matters: use permutations nPr.
2. A bag has 7 red and 2 blue counters. Two are taken with replacement. What is the probability both are red? Give a fraction in simplest form. → 49/81Prompt: Multiply along the branches of the tree diagram.
3. Leo has 5 different books to put on a shelf. In how many different orders can they be arranged? → 120Prompt: How many choices for the first spot, then the second…?

• Take a quick class survey (favorite fruit, travel to school) and ask what the results tell us.
• Share the objective: Binomial probability. Read the success criteria together.

• Work through the example out loud, saying why you do each step, not just what you do.
• Example: A trial succeeds with probability 0.4. It is repeated 6 times independently. What is the probability of exactly 5 successes? Round to 3 decimal places.
• Step 1: 6 × 0.4^5 × 0.6^1
• Step 2: ≈ 0.037
• Answer: 0.037
• Pause after each step and ask a student to say what comes next.

• Do these together. Students try each step on whiteboards before you reveal it.
• Use the hints as prompts rather than giving the answer.

1. A trial succeeds with probability 0.5. It is repeated 6 times independently. What is the probability of exactly 1 success? Round to 3 decimal places. → 0.094Prompt: P(X = k) = nCk × p^k × (1 − p)^(n − k).
2. A trial succeeds with probability 0.4. It is repeated 3 times independently. What is the probability of exactly 2 successes? Round to 3 decimal places. → 0.288Prompt: P(X = k) = nCk × p^k × (1 − p)^(n − k).

• Students work on the student sheet. Circulate and check the first two answers of every student early.
• Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

• Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.

1. A trial succeeds with probability 0.5. It is repeated 5 times independently. What is the probability of exactly 4 successes? Round to 3 decimal places. → 0.156Prompt: P(X = k) = nCk × p^k × (1 − p)^(n − k).
2. A trial succeeds with probability 0.5. It is repeated 3 times independently. What is the probability of exactly 2 successes? Round to 3 decimal places. → 0.375Prompt: P(X = k) = nCk × p^k × (1 − p)^(n − k).

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-12.