Question 1: List all possible outcomes when flipping a coin and rolling a six-sided die. Use systematic listing to ensure no outcomes are missed.

Answer: ["H1","H2","H3","H4","H5","H6","T1","T2","T3","T4","T5","T6"]

Question 2: A bag contains red, blue, and green balls. If two balls are drawn without replacement, list all possible ordered outcomes for the colours.

Answer: ["Red-Red","Red-Blue","Red-Green","Blue-Red","Blue-Blue","Blue-Green","Green-Red","Green-Blue","Green-Green"]

Question 3: Construct a systematic list of all possible two-letter arrangements using the letters A, B, and C, without repetition.

Answer: ["AB","AC","BA","BC","CA","CB"]

Question 4: List all outcomes when rolling two dice and recording the sum of the numbers. Use systematic listing to cover all possibilities.

Answer: ["2","3","4","5","6","7","8","9","10","11","12"]

Question 5: A spinner is divided into three equal sectors numbered 1, 2, and 3. List all possible outcomes when spinning twice, using systematic listing.

Answer: ["1-1","1-2","1-3","2-1","2-2","2-3","3-1","3-2","3-3"]

Question 6: A student draws a card from a deck containing only the cards A, B, C, and D. They record their outcomes for 3 successive draws, replacing the card each time. List all possible outcomes.

Answer: ["AAA","AAB","AAC","AAD","ABA","ABB","ABC","ABD","ACA","ACB","ACC","ACD","ADA","ADB","ADC","ADD","BAA","BAB","BAC","BAD","BBA","BBB","BBC","BBD","BCA","BCB","BCC","BCD","BDA","BDB","BDC","BDD","CAA","CAB","CAC","CAD","CBA","CBB","CBC","CBD","CCA","CCB","CCC","CCD","CDA","CDB","CDC","CDD","DAA","DAB","DAC","DAD","DBA","DBB","DBC","DBD","DCA","DCB","DCC","DCD","DDA","DDB","DDC","DDD"]

Question 7: Explain why systematic listing is useful in probability, and give an example of a situation where it would help avoid missing outcomes.

Answer: Systematic listing helps ensure no outcomes are missed, especially in cases with multiple factors. For example, listing all possible combinations when selecting toppings for a pizza from three options (pepperoni, mushrooms, peppers) ensures you consider every combination, such as only pepperoni, pepperoni and mushrooms, etc.

Question 8: A box contains 4 different coloured balls. If you pick 2 balls in order without replacement, how many different outcomes are possible? List them systematically.

Answer: ["Color1-Color2","Color1-Color3","Color1-Color4","Color2-Color1","Color2-Color3","Color2-Color4","Color3-Color1","Color3-Color2","Color3-Color4","Color4-Color1","Color4-Color2","Color4-Color3"]

Question 9: Identify a common mistake students make when listing outcomes systematically and explain how to correct it.

Answer: A common mistake is omitting some outcomes, such as forgetting to list all combinations when multiple factors are involved. To correct this, students should systematically list each factor's possibilities for every option of the other factors, ensuring complete coverage.

Question 10: Challenge: A password is formed from 2 letters followed by 1 digit. Letters can be A, B, C, D and digits 0-2. List all possible passwords systematically.

Answer: ["A-A-0","A-A-1","A-A-2","A-B-0","A-B-1","A-B-2","A-C-0","A-C-1","A-C-2","A-D-0","A-D-1","A-D-2","B-A-0","B-A-1","B-A-2","B-B-0","B-B-1","B-B-2","B-C-0","B-C-1","B-C-2","B-D-0","B-D-1","B-D-2","C-A-0","C-A-1","C-A-2","C-B-0","C-B-1","C-B-2","C-C-0","C-C-1","C-C-2","C-D-0","C-D-1","C-D-2","D-A-0","D-A-1","D-A-2","D-B-0","D-B-1","D-B-2","D-C-0","D-C-1","D-C-2","D-D-0","D-D-1","D-D-2"]