Probability: count outcomes only after checking the assumptions
For equally likely elementary outcomes, an event’s theoretical probability is its favourable-outcome count divided by the total-outcome count.
For equally likely elementary outcomes, an event’s theoretical probability is its favourable-outcome count divided by the total-outcome count.
The assumption comes first
NCERT distinguishes theoretical probability from observed relative frequency. The simple counting formula requires equally likely elementary outcomes. Naming two categories does not automatically give each a probability of one half.
For example, a bag can contain unequal numbers of objects of two colours. The colour labels are two categories, but the elementary draws can favour one colour because more objects carry it.
An original draw example
Imagine five identical-feeling counters: three green and two yellow. If each counter has an equal chance of being drawn, the probability of green is 3/5 and yellow is 2/5. The probabilities add to one.
This hypothetical model assumes random selection and equally likely individual counters. Without that assumption, simply counting their colours may not describe the actual selection process.
Do not promise a fixed short-run result
A probability of 3/5 does not guarantee exactly three green results in the next five independent draws with replacement. A model describes likelihood, while a short observed sequence can vary. Keep the theoretical claim separate from an experimental count.
For an original revision task, write the sample outcomes individually before grouping those favourable to an event. Then ask whether each elementary outcome is equally likely. This prevents the denominator from becoming the number of category names rather than the number of relevant outcomes.
A fair die supplies six equally likely faces, but an event can include several faces. State the event clearly before counting it. This static mathematics explainer is not a prediction about games of chance or advice to gamble, and its examples are not measured data.
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Frequently asked questions
Do two named categories necessarily each have probability one half?
No. Their underlying outcomes may not be equally numerous or equally likely.
Does probability guarantee the exact next short sequence?
No. It describes likelihood under a model.