Abiologist diluted a blood sample with distilled water.
while observing the sample under a microscope, she
noted that the red blood cells burst. this bursting is
most likely the result of which process?

When blood sample is diluted with distilled water ,RBC  burst because of the movement of water molecule from outside to inside the cells. This is due to osmosis.

Explanation:

Osmosis- Osmosis is a process of movement of water molecules from its higher concentration to  lower concentration through a semipermeable membrane.

This is a passive process. based on dissolved solutes in liquid , osmotic pressure gradient generates and this gradient allows liquid molecule to move from higher concentration of liquid to lower concentration. Movement of liquid molecules continues till osmotic gradient meets to the equilibrium in and out of the cell.

On the basis of dissolved solutes in liquid there are 3 types of solution.

1- Hypertonic solution- In this solution the solute concentration  is higher than inside the cell. If cell is placed in this solution water molecules move  from cell to the outer medium ,makes cell to shrink. in case of RBC this is known as CRENATION.

2- Hypotonic solution- In this solution the solute concentration is lower than inside the cell. So if cell is placed in this solution ,water molecule moves from outer medium to inside the cell. It will make cell swell and burst. (That is the case with RBC asked in question)

3- Isotonic solution- In this solution concentration of solute inside cell and outside medium is same . No movement of liquid molecule will occur, as the osmotic gradient will be same.