AI generatedProbabilityKey Stage 3

Systematic lists of combined outcomes

Systematic lists of combined outcomes.

  • Probability = favourable outcomes ÷ all outcomes when individual outcomes are equally likely.
  • A probability lies between 0 and 1; complementary probabilities sum to 1.
  • Experimental relative frequency estimates probability and can vary between samples.

Example 1

Spinner A has numbers 1 to 2, and spinner B has numbers 1 to 2. List all ordered outcomes (A, B).

(1, 1); (1, 2); (2, 1); (2, 2).

Fix the first value while listing every second value, then move to the next first value. There are 4 outcomes.

Example 2

Spinner A has numbers 1 to 3, and spinner B has numbers 1 to 2. List all ordered outcomes (A, B).

(1, 1); (1, 2); (2, 1); (2, 2); (3, 1); (3, 2).

Fix the first value while listing every second value, then move to the next first value. There are 6 outcomes.

Your turn

Question 1

Spinner A has numbers 1 to 4, and spinner B has numbers 1 to 2. List all ordered outcomes (A, B).

Check answer
(1, 1); (1, 2); (2, 1); (2, 2); (3, 1); (3, 2); (4, 1); (4, 2).

Fix the first value while listing every second value, then move to the next first value. There are 8 outcomes.

Question 2

Spinner A has numbers 1 to 5, and spinner B has numbers 1 to 2. List all ordered outcomes (A, B).

Check answer
(1, 1); (1, 2); (2, 1); (2, 2); (3, 1); (3, 2); (4, 1); (4, 2); (5, 1); (5, 2).

Fix the first value while listing every second value, then move to the next first value. There are 10 outcomes.

Question 3

Spinner A has numbers 1 to 2, and spinner B has numbers 1 to 3. List all ordered outcomes (A, B).

Check answer
(1, 1); (1, 2); (1, 3); (2, 1); (2, 2); (2, 3).

Fix the first value while listing every second value, then move to the next first value. There are 6 outcomes.

Question 4

Spinner A has numbers 1 to 3, and spinner B has numbers 1 to 3. List all ordered outcomes (A, B).

Check answer
(1, 1); (1, 2); (1, 3); (2, 1); (2, 2); (2, 3); (3, 1); (3, 2); (3, 3).

Fix the first value while listing every second value, then move to the next first value. There are 9 outcomes.

Question 5

Spinner A has numbers 1 to 4, and spinner B has numbers 1 to 3. List all ordered outcomes (A, B).

Check answer
(1, 1); (1, 2); (1, 3); (2, 1); (2, 2); (2, 3); (3, 1); (3, 2); (3, 3); (4, 1); (4, 2); (4, 3).

Fix the first value while listing every second value, then move to the next first value. There are 12 outcomes.

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