Binomial Distribution:

A binomial distribution is a probability distribution that describes the number of successful outcomes in a fixed number of independent trials, where the probability of success is constant. It is used to analyze data that has two possible outcomes, such as success or failure, yes or no, or heads or tails.

Modes in a Distribution:

A mode is the value that appears most frequently in a distribution. In other words, it is the peak of the distribution. A distribution can have one or more modes.

Modes in a Binomial Distribution:

In a binomial distribution, the probability of success is constant, and the number of trials is fixed. Therefore, the distribution can have one or more modes, depending on the values of the parameters.

- One Mode: If the probability of success is close to 0 or 1, the distribution will have one mode. This is because the majority of the trials will either be successes or failures, and the probability of the opposite outcome will be very low.
- Two Modes: If the probability of success is between 0 and 1, the distribution can have two modes. This is because there will be two values of the number of successes that are most likely to occur.

Conclusion:

Therefore, the correct answer is option D, which states that a binomial distribution may have one or two modes. The presence of modes in a binomial distribution depends on the values of the parameters, and it can have one or more modes.