Restrict the possibilities
Work with conditional probability and necessary conditions.
The idea
Given information changes the sample space. A rule of the form membership implies induction can be reversed only as a contrapositive, not as a simple converse.
A method to try
- List the outcomes still possible after the condition.
- For a logical rule, test whether an alleged conclusion could fail.
Follow the reasoning.
A card is drawn uniformly from cards numbered 1 to 8. You are told that its number is greater than 5. What is the chance that the number is even?
- The information removes 1 through 5 from consideration. The remaining equally likely outcomes are 6, 7 and 8.
- Two of these three numbers are even, so the conditional probability is 2/3. The original eight-card denominator no longer describes the conditioned sample space.
- Write the reduced set before calculating. This is especially useful when an intuitive answer such as one half describes the original selection but not the selection after new information.
Think it through first.
All certified samples passed inspection. A sample failed inspection. Can it be a certified sample under the rule?
Show the explanation
No.
This is the contrapositive of the rule. Passing inspection alone would not prove certification.
Make it your own
After reading, explain the method in your own words and identify the condition that makes it valid. Then try the linked starter practice without referring back to the worked example. Review the reasoning behind an error before repeating the same item; remembering an answer is different from being able to solve a new problem.
This lesson is one part of a short starter pathway. It does not cover the full exam syllabus or establish a predicted score.
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