If the number of trials increases in a binomial distribution increases, both the expected value and standard deviation tend to rise. The expected value increases linearly with the number of trials, reflecting the greater likelihood of success, while the standard deviation increases more slowly, indicating a proportionally smaller increase in variability with each additional trial.

As the number of trials increases in a binomial distribution, the expected value (mean) increases proportionally. The increase in the expected value occurs because, with more trials, the total number of successes (n * p) is likely to be larger, contributing to a higher average outcome. The expected value () of a binomial distribution is calculated using the formula = n * p, where n is the number of trials and p is the probability of success on a single trial. When the number of trials increases, the overall likelihood of success (n * p) becomes larger, leading to a higher expected value.

The increase in standard deviation is associated with the fact that with more trials, there is a greater variability in possible outcomes. However, the rate of increase is slower due to the square root term in the standard deviation formula, resulting in a diminishing impact on variability as the number of trials grows. The standard deviation () of a binomial distribution is calculated using the formula = (n * p * (1 - p)). As the number of trials increases, the standard deviation tends to increase as well. However, the rate at which it increases diminishes. While the expected value increases linearly with the number of trials, the standard deviation increases more slowly, resulting in a relatively smaller increase in variability compared to the increase in the expected value.