What function attempts to predict the probability that a binary or ordinal target will acquire the event of interest?

The function that is used to predict the probability of a binary or ordinal target acquiring the event of interest is the logistic function. This model is particularly well-suited for outcome variables where the response can only take on two possible values (such as "yes" or "no") in the case of binary targets. For ordinal targets, it can handle multiple categories while respecting the order among them.

Logistic regression works by estimating the probabilities using the logistic function, which maps any real-valued number into the range of 0 to 1, making it ideal for probability predictions. It transforms the linear combination of independent variables into a probability that something will happen, thus facilitating the prediction of event occurrence based on input features.

In contrast, the linear function is generally used for continuous outcomes and does not handle the probability outputs required for binary classification effectively. The exponential function is typically applied in contexts where growth rates are modeled, and while it is fundamental in various statistical distributions, it does not suit direct probability estimation for binary/ordinal events. The polynomial function, while it can model relationships between variables, is not specifically designed to output probabilities in the way a logistic model does.

Therefore, the logistic function is the correct choice for predicting probabilities in binary or ordinal outcomes.