Purity asks how much of the coincidence total is true signal. The toy rates add
4 hertz true plus 12 hertz accidental to make 16 hertz total, so the purity is
4/16 or 1/4; real purity estimates depend on background subtraction, window
choice, detector efficiency, timing resolution, and uncertainty.
True coincidences and accidentals form a checked fraction. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
True and accidental rates add
A true rate of 4 hertz plus 12 hertz accidentals gives 16 hertz total.