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The mathematical technique used to investigate the statistical law governing random events in the natural world is known as probability statistics. People's attention has been drawn more and more to probability statistics as science and technology have advanced. These statistics are widely used in daily life, the national economy, and industrial and agricultural production. This study addresses the use of probability statistics to solving practical problems, primarily focusing on the pertinent understanding of Bernoulli scheme, normal school, and mathematical expectation. The mathematical possibility that something will occur is known as probability, and it is utilized in many daily applications such as weather forecasts, athletics tactics, sports and leisure activities, and business planning. Probability theory is used in daily life, particularly in risk management and financial market trading. The main thing that citizens should know is how probability estimates are formed and how they affect decisions. Probably the only companies that base their whole business strategy on chance are the big insurance companies. Reliability is a key area in which probability theory is applied in real-world situations. In real life, probability and the capacity to comprehend and calculate the chance of any given set of possible events are crucial.