The potential that a child who pricked her finger with a syringe found in a school yard could be exposed to the HIV/AIDS virus is minuscule, a state health official said.

However, the child's parents are taking precautionary steps to protect the 12-year-old girl against acquired immune deficiency syndrome and other diseases that can be passed by syringes.The girl, a sixth-grader at Mountain View Elementary, 1315 S. California Ave., pricked her right thumb Monday when she dropped the syringe and attempted to pick it up again. She and four other students discovered the discarded needle on the school playground, police reports show.

The Salt Lake School District is investigating the incident and has put a teacher aide on leave pending the outcome, said Sherry Clark, district spokeswoman.

The aide reportedly asked the children to pick up the syringe when they told her about it. The child's parents believe the aide acted unwisely and have retained a lawyer to protect them in case of any adverse outcome.

Geoff Wertzberger, director of the Bureau of HIV/AIDS Prevention and Control in the State Health Department, said the risk of contracting disease from contact with a contaminated needle is extremely small. How long the needle had been on the playground after use and how deep the wound the child suffered are factors, he said.

The HIV virus does not survive long when exposed to air, and a deep wound is more likely to cause an infection, Wetzberger said. The Mountain View child reportedly was wounded deeply enough to draw blood.

The likelihood of other diseases passed by needles is greater than AIDS, he said. The young victim is being given preventive immunizations for hepatitis, the most likely disease to result from her exposure if the needle had been discarded by an individual at risk for AIDS.

Wertzberger said a very small number of AIDS cases have resulted nationally from accidental needle pricks, mostly among health professionals who have significant exposure to the disease among patients.

IV drug abusers, however, are at high risk. Centers for Disease Control figures through March 1991 show that 37,090 cases of AIDS have been attributed to the use of shared or otherwise contaminated needles in this group, Wertzberger said.