In civil cases, a judge often determines liability on the balance of probability rather than the criminal standard of beyond a reasonable doubt.

In the lecture, she compared several probability distributions to determine which model best fit the data.

Before analyzing the data, the researchers specified the prior probabilities for each model to ensure fair comparison.

The analyst updated the posterior probabilities for all competing models after incorporating the new evidence.

When analyzing sensor outputs, the probability densities often reveal multimodal behavior that simple statistics miss.

The students calculated the experimental probabilities of each outcome after conducting fifty coin tosses.

In quantum mechanics, probability amplitudes determine the interference patterns observed in experiments.

Historians often weigh competing balances of probabilities when reconstructing events from sparse records.

To accurately model the system, we must estimate the joint probabilities of temperature and pressure across all sensors.

To improve their diagnostic models, data scientists estimated conditional probabilities from the clinical dataset and used them to update prior beliefs.