Theory of probability can be applied to

Explanation:

• Probability theory applies to accidental (random) errors because they are unpredictable and follow statistical distribution.
• The theory helps in quantifying the likelihood of different error magnitudes, allowing engineers and scientists to estimate precision and reliability of measurements.

• hese errors occur due to unknown and unpredictable factors such as fluctuations in measuring conditions, limitations of instruments, and variations in human observation.

• The magnitude and sign of accidental errors vary randomly from one measurement to another — some errors may be positive, others negative.

• They follow a certain statistical distribution, commonly a normal distribution, which makes probability theory applicable for analyzing their pattern.

• With multiple measurements, the impact of accidental errors can be minimized through averaging and statistical treatment, improving the accuracy of results.

 Additional Information

Cumulative (Systematic) Errors:

• Cumulative errors are consistent errors that occur in a fixed pattern, often increasing or decreasing steadily with time or distance.

• They arise from defects in equipment, errors in calibration, observer bias, or faulty methods of observation or measurement.

• Unlike accidental errors, cumulative errors do not vary randomly and hence cannot be analyzed or corrected using probability theory.

• These errors must be identified and corrected through proper calibration, adjustment of equipment, or refining observation techniques.