Two, three, and four-outcome wavefunctions all close the same exact probability budget. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Normalization already held for two outcomes

Chapter one's two-outcome states close their probability budget with two terms. This row repeats that exact rule as the scan's baseline.

925+1625=1\frac{9}{25}+\frac{16}{25}=1
Two-outcome wavefunctionTwo exact terms close the budget.left3/59/25right4/516/25

The same rule holds for three and four outcomes

Normalization is not special to two-outcome systems. Adding a third or fourth exact term still closes the same probability budget at one, as long as the squared amplitudes are computed exactly and added.

outcomestermssumtwo21three31four41\begin{array}{c|c|c}\text{outcomes}&\text{terms}&\text{sum}\\\text{two}&2&1\\\text{three}&3&1\\\text{four}&4&1\\\end{array}
Three-outcome wavefunctionThree exact terms still close the same budget.left2/34/9mid2/34/9right1/31/9

Four equal terms still close the budget exactly

The four-outcome row splits the budget into four equal exact quarters. The rule that closed the two-outcome budget in chapter one closes this one too.

14+14+14+14=1\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=1
Four-outcome wavefunctionFour equal exact terms close the budget.a1/21/4b1/21/4c1/21/4d1/21/4