Use the Trials Actually Observed

Supplied materials

• Paper or a browser scratch area; a calculator is optional unless rounding is requested.
• Supplied teaching case: A model trial succeeds 5 times in 40 attempts. What is the experimental success proportion? Candidate answers: (A) 1/7 (B) 1/8 (C) 7/8 (D) 8.
• Independent check inputs: A model trial succeeds 6 times in 40 attempts. What is the experimental success proportion? Candidate answers: (A) 17/20 (B) 20/3 (C) 3/17 (D) 3/20.

Learn the idea

A complete population, a selected sample and a probability model are different sources of information. Sampling supports estimates, observed trial counts support experimental proportions, and explicit independence permits multiplication of model probabilities. An experimental proportion describes successful outcomes in a supplied trial record. It uses all attempts in the denominator and can differ from a theoretical probability based on an ideal model.

Here is the method on the supplied teaching case. Divide observed successes by all attempts: 5/40=1/8. This proportion describes the supplied record and does not guarantee future trial results.

A small supplied record does not guarantee the next outcome. Keep successes and attempts distinct, and do not treat a failure count as the success denominator or round away meaningful fraction information.

1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
3. Solve the independent check with its changed inputs before revealing feedback.
4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.

Check your reasoning

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Take it further

Changed-input task: A model trial succeeds 12 times in 40 attempts. What is the experimental success proportion? Candidate answers: (A) 10/3 (B) 3/10 (C) 3/7 (D) 7/10. Show the mathematical reason, not only the selected answer. Expected result: 3/10. Divide observed successes by all attempts: 12/40=3/10. This proportion describes the supplied record and does not guarantee future trial results.

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