Logistic Regression:

Logistic regression is used with binary data when you want to model the probability that a specified outcome will occur. Specifically, it is aimed at estimating parameters a and b in the following model:

where p_i is the probability of a success for given value x_i of the explanatory variable X.

Use of the log of the odds p/(1-p) (the logit) guarantees that the predicted value of p will always be between 0 and 1.