lesson
List the whole sample space
1 · Learn
For two independent fair coin tosses, the ordered outcomes are HH, HT, TH and TT. Exactly one head occurs in two of the four equally likely outcomes. A list prevents overlooking order or counting an outcome twice.
Independence and equal likelihood are assumptions to check, not decorations. Different experiments may need different outcome probabilities, so a simple count is not always sufficient.
2 · Worked example
Exactly one head has probability 2/4 = 1/2. At least one head has probability 3/4, a different event that also includes HH.
3 · Your turn
For two independent fair coin tosses, find the probability of no heads and of at least one head.
Check your answer
1/4 and 3/4 respectively.
4 · Apply your learning
Make a table for a fair coin and a fair six-sided die, then identify an event and count its outcomes systematically.
Adult guidance and safety
Ask for the reasoning and a check, not only a numerical result. Supply accurate diagrams, coordinate grids and data displays where required. Use varied examples and revisit prerequisite gaps; these short teaching models are not a completed assessment programme.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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