AC9M4P02 • Homework

Repeated Chance Experiments and Variation worksheet

Use this printable homework sheet for written working, application and reflection alongside the online learning activities.

Open practice

Eight written and practical homework tasks

Keep actual records. Ask an adult to review the evidence; a completion tick alone is not mastery.

  1. Toss a coin in two sets of 12 trials. Record sequences and tallies, compare counts and write what the result does not tell you about the next toss.

    Working: ____________________________________________________

  2. Roll a die 15 times. Make a six-face frequency table including zeros. Order the observed counts and describe any ties.

    Working: ____________________________________________________

  3. Two labelled coins produced HH 5, HT 6, TH 4, TT 3. Find total trials, mixed outcomes and matching outcomes; explain why HT and TH are separate.

    Working: ____________________________________________________

  4. Conduct 18 two-coin trials yourself. Keep all four categories and compare your results with the example in question 3 without claiming they must match.

    Working: ____________________________________________________

  5. Draw a card from a standard deck without jokers, record suit and type, return and shuffle. Repeat 8 times. Use picture J/Q/K, numbered 2–10, and ace.

    Working: ____________________________________________________

  6. Play four Noughts and Crosses games, alternating who starts. Record wins/draws and explain one strategic move and one limit of your conclusion.

    Working: ____________________________________________________

  7. Play First to 20 twice: begin 0, alternate adding 1 or 2, reach 20 exactly to win; swap starter. Keep move records. Explain the winning choice at 18 and at 19.

    Working: ____________________________________________________

  8. With an adult, use a virtual coin for 12 trials and compare with 12 physical tosses. Explain how random examples can help AI training and why checking remains necessary.

    Working: ____________________________________________________

Worked answers and adult review guide

  1. Each set totals 12 and agrees with its sequence. Report actual counts and similarities/differences; no forced next result follows. Adult checks actual work.

  2. All six faces appear as table labels, counts total 15 and match actual records. Ordering and ties follow the observed data, not expected equal frequencies.

  3. Total 18; mixed 6+4=10; matching 5+3=8. HT and TH identify which labelled coin showed heads. Require correct sums and explanation.

  4. Four counts total 18 and match real outcomes. Compare the category counts with the 18-trial example; equal trial totals make the counts directly comparable. Different observed counts can occur even with the same stated chances.

  5. Each suit and type table separately totals 8. Check actual card records and classification; consistent replacement restores the starting deck. Accept observed variation.

  6. Two starts each; four complete game records. A specific block or line-making move is valid. Few games and different choices/skill limit a claim about going first.

  7. Every move adds 1 or 2, ending at 20. At 18 add 2; at 19 add 1. Inspect both games and swapped starts; do not infer guaranteed advantage from two results.

  8. Both sets have actual 12-result records. Matching stated chances do not require matching sequences. Random sampling can supply varied examples, but accuracy and conclusions still require checking.