SM3.4 Probability
You can compute the probability of an event as favourable outcomes over equally likely total outcomes, and handle questions about cards, dice and complementary events.
Topics shown in module order.
Probability here is a fraction: the outcomes you want over all the outcomes there are, provided every outcome is equally likely. That proviso is the chapter's one subtlety, and dice, coins and a well-shuffled deck are used because they honour it. The complement rule, that the chance of a thing and of its absence add to one, halves the work of many questions and is the chapter's most reused idea.
Work through these
List the full outcome set for one die, two coins, and a card drawn from a deck, before any probability is computed
Every error in this chapter is a miscounted outcome set. Listing the set explicitly, fifty-two cards, four suits, is slow the first time and automatic afterwards, which is the right order.
Compute probabilities for single events across dice, coins and cards
The fraction is always the same move; what varies is the counting above and below it. A spread of settings is what turns the definition into a reflex that transfers to settings you have not seen.
Use the complement rule on questions phrased with not or at least
The probability of at least one is usually painful directly and trivial through its complement. Recognising the phrasing that signals the shortcut is a skill examinations reward every single year.
Explain with one example why unequal outcomes break the formula
Rain or no rain tomorrow is two outcomes but not a half chance of each. Owning one clean counterexample is what keeps the formula from being applied where its one condition fails.
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