Final answer:
Water beads up on oily skin because cohesive forces within water surpass the adhesive forces between water and oil, while on unoiled skin, greater adhesive forces cause water to spread, not bead.
Step-by-step explanation:
Water beads up on an oily sunbather but does not on her neighbor's unoiled skin due to the different interactions of cohesive and adhesive forces involved. Water forms beads on oily skin because the cohesive forces within the water are stronger than the adhesive forces between the water and the oily substance. Since cohesion encourages water molecules to stay together rather than adhere to the oil, the water forms beads. In contrast, on unoiled skin, the adhesive forces between water and the skin are stronger, causing the water to spread out rather than form beads.