Home Learning: Probability and Likelihood

Subject: Mathematics | Year: 7

Estimated Time: 30–40 Minutes Name: _________________________ Class/Set: ____________ Due Date: ____________

The Purpose

Why are we doing this? To develop your ability to list all possible outcomes of an event systematically using tables and diagrams, ensuring no result is missed when calculating probabilities.

Instructions

1. Construct: In your exercise book, draw a sample space diagram (a table) to show all the possible outcomes for a 'Meal Deal'. You must choose one main and one side.

   • Mains: Sandwich (S), Wrap (W), Pasta (P).
   • Sides: Apple (A), Crisps (C).

2. Calculate: Use your table from Instruction 1 to find the probability of a student choosing:

   • a) ☐ A Wrap and Crisps.
   • b) ☐ Any meal that includes an Apple.
   • c) ☐ A Sandwich and any side.

3. Construct: Draw a sample space diagram to show the possible totals when two fair four-sided dice (numbered 1, 2, 3, and 4) are rolled and their scores are added together.

4. Calculate: Use your table from Instruction 3 to find the probability of:

   • a) ☐ Scoring a total of exactly 5.
   • b) ☐ Scoring a total of more than 6.
   • c) ☐ Scoring an even total.

Success Criteria (Checklist)

☐ I have used a ruler and pencil to draw neat tables for my sample space diagrams. ☐ I have correctly identified the total number of outcomes for each scenario. ☐ I have expressed my probabilities as fractions in their simplest form.

Challenge / Extension (Optional)

• Investigate: If you were to flip a coin AND roll a six-sided die, how many total outcomes would there be? Write a sentence explaining the quickest way to work out the total number of outcomes without drawing the whole table.

---

⚠ TEACHER’S GUIDANCE & MARK SCHEME (DO NOT PRINT FOR STUDENTS)

---

Teacher’s Post-Task Briefing

1. Model Answers / Expected Outcomes

Instruction 1: Meal Deal Table

	Apple (A)	Crisps (C)
Sandwich (S)	S, A	S, C
Wrap (W)	W, A	W, C
Pasta (P)	P, A	P, C

Instruction 2 Answer:

• a) ☐ 1/6
• b) ☐ 3/6 (or 1/2)
• c) ☐ 2/6 (or 1/3)

Instruction 3: Dice Addition Table

+	1	2	3	4
1	2	3	4	5
2	3	4	5	6
3	4	5	6	7
4	5	6	7	8

Instruction 4 Answer:

• a) ☐ 4/16 (or 1/4)
• b) ☐ 3/16
• c) ☐ 8/16 (or 1/2)

Challenge Answer: 12 outcomes (2 × 6). The quickest way is to multiply the number of outcomes of the first event by the number of outcomes of the second event (Product Rule).

2. Common Misconceptions to Flag

• Incomplete Lists: Students often miss one or two outcomes if they do not use a table. Emphasise that the table is a 'safety net' for accuracy.
• Denominator Errors: Students may use the number of rows or columns as the denominator instead of the total number of cells (the product of the dimensions).
• Summation vs. Listing: In Instruction 3, ensure students are adding the scores (1+1, 1+2) rather than just listing the pairs (1,1).

3. Classroom Discussion Starters (The 'Journey')

• The Diagonal Pattern: Look at the dice total table. Why do the same totals appear in diagonal lines?
• Predicting Outcomes: If we added a third side to the meal deal (e.g., Yoghurt), how many extra outcomes would that create? Can we see a pattern between the number of items and the total outcomes?
• Real-world Logic: Where else might we need to list every possible outcome? (e.g., combinations for a bike lock, or possible results in a sports tournament).