Make devices fair from experimental results practice

With $5$ equally likely colors, each should appear about $\dfrac{400}{5}=80$ times ($20\%$). Green appeared only $52$ times ($13\%$), so there are too few green chips, and purple appeared $98$ times ($24.5\%$), so there are too many purple chips. Replacing some purple chips with green chips fixes both imbalances at once.

Three equal sections should each be chosen about $\dfrac{300}{3}=100$ times ($33\%$). Strength was chosen $145$ times ($48\%$), so its section is too large, and Flexibility was chosen only $67$ times ($22\%$), so its section is too small. Moving area from Strength to Flexibility corrects both the over- and under-represented stations.

Five equal lanes should each produce about $\dfrac{200}{5}=40$ winners ($20\%$). Lane 4 produced $58$ winners ($29\%$), so its lane is too wide, and lane 5 produced only $23$ winners ($11.5\%$), so its lane is too narrow. Shifting width from lane 4 to lane 5 rebalances both lanes at once.

Four equal lanes should each receive about $\dfrac{250}{4}=62.5$ marbles ($25\%$). Lane Z received $87$ marbles ($34.8\%$), so its opening is too wide, and lane W received only $49$ marbles ($19.6\%$), so its opening is too narrow. Narrowing lane Z while widening lane W shifts marble flow from the over-used lane to the under-used one on the shared divider panel.

Three equal sections should each be drawn about $\dfrac{900}{3}=300$ times ($33\%$). Section B was drawn only $255$ times ($28.3\%$), so its pick-up opening is too small, and section C was drawn $333$ times ($37\%$), so its opening is too large. Enlarging the opening for section B by shrinking the opening for section C shifts access from the over-favored section to the under-favored one.

Four equal gates should each release about $\dfrac{500}{4}=125$ times ($25\%$). Chamber B was selected only $82$ times ($16.4\%$), so its gate is too narrow, and chamber D was selected $163$ times ($32.6\%$), so its gate is too wide. Widening the gate for chamber B by narrowing the gate for chamber D shifts release space from the over-used chamber to the under-used one on the shared release bar.

A fair die should show each face about $\dfrac{600}{6}=100$ times ($\dfrac{1}{6}$). Face $6$ appeared $140$ times ($23.\overline{3}\%$), so the padding on face $6$ makes it too likely. Face $1$ appeared only $72$ times ($12\%$), so it lacks enough padding. Moving padding from face $6$ to face $1$ lowers the over-represented face while raising the under-represented one.

Each face should land about $\dfrac{400}{6}\approx 67$ times ($\dfrac{1}{6}$). Face $2$ appeared only $48$ times ($12\%$), so it lacks enough padding, and face $1$ appeared $76$ times ($19\%$), so it has too much. Moving padding from face $1$ to face $2$ raises the under-represented face while lowering the over-represented one.