[Verse 1] Sarah flips a coin at breakfast time Heads or tails, each outcome's prime Fifty-fifty split divides the space Sample space contains each possible case Events are subsets we define with care Mutually exclusive means they never share [Chorus] Add when events can't happen together Multiply when they're linked like tethered weather P of A plus P of B, minus overlap you see That's the addition rule's decree P of A times P of B, when independence runs free Multiplication's harmony [Verse 2] Rolling dice, the outcomes dance Six faces give each number chance When events share common ground Intersection must be found Union means at least one occurs Complement flips what probability infers [Chorus] Add when events can't happen together Multiply when they're linked like tethered weather P of A plus P of B, minus overlap you see That's the addition rule's decree P of A times P of B, when independence runs free Multiplication's harmony [Bridge] Given information changes everything we know Conditional probability makes the numbers flow P of A given B equals intersection's share Divided by P of B, handle with special care Total probability breaks down the maze Partition sample space in non-overlapping ways [Verse 3] Tom draws cards without replacement Each draw shifts the next event's placement First card Ace, now fifty-one remain Three Aces left, the odds have changed their reign Bayes' theorem flips the question round Prior times likelihood, normalization's sound [Chorus] Add when events can't happen together Multiply when they're linked like tethered weather P of A plus P of B, minus overlap you see That's the addition rule's decree P of A times P of B, when independence runs free Multiplication's harmony [Outro] Probability's foundation built on logic's frame Addition, multiplication, conditional game Master these rules and watch uncertainty bend To mathematical precision that never pretends
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