lesson
Choose the relevant denominator
1 · Learn
A conditional probability restricts the sample space to cases satisfying a stated condition. In a table, first identify that group, then count the desired cases within it. Using the whole population denominator answers a different question.
Read 'given that' carefully. A probability within a group need not equal the probability of selecting both characteristics from the whole population.
2 · Worked example
Given a pupil is in A, probability of pass is 6/10. Selecting an A pupil who passed from all 20 gives 6/20.
3 · Your turn
Using the supplied table, find probability of pass given group B.
Check your answer
3/10.
4 · Apply your learning
Compare conditional and joint questions using the same table and label each denominator.
Adult guidance and safety
Check prerequisites, units and reasoning. Provide accurate diagrams and varied practice. Extension content needs suitable prior understanding; no GCSE board, tier or examination readiness is implied by this proposed sequence.
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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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