You *probably* wonder how **predicted probability** is different from normal probability. After all, that is why you’re here. Well, it has to do with how the probability is calculated and what the outcomes mean. Well, a predicted probability is, essentially, in its most basic form, the probability of an event that is calculated from available data.

## Basic Predictions

In the initial stages of predicting probability, you use the simple probabilities of a few events occurring in some combination.

### Mutually Exclusive Events

What is the probability of rolling two consecutive sixes using a fair die? In this case, we use the fact that rolling a fair die is a mutually exclusive event.

The probability of rolling a single six is 0.16. Therefore, the probability of rolling *two* sixes is the product of the individual probabilities.

*P*(6) x *P*(6) = 0.16 x 0.16 = 0.028

### Dependent Events

The calculations for dependent events are similar to those for mutually exclusive events. Of course, we have to consider how one event affects the next.

What is the probability of drawing two from a standard deck of cards without replacement? First, the probability of drawing the first queen is

*P*(Q) = 4 ÷ 52 = 0.077

But the probability of drawing a second queen is different because now there are only three queens and 51 cards.

*P*(second Q) = 3 ÷ 51 = 0.059

The probability is still the product of the two probabilities

*P*(Q, Q) = 0.077 x 0.059 = 0.0045

## Probability and Regression

So far, we have discussed the probability of single events occurring. However, what if you wanted to figure out the probability of more complex complementary events occurring? For example, the probability of dropping out of school based on sociodemographic information, attendance, and achievement. In this case, we have several indicators and complementary events.

One way that we calculate the predicted probability of such binary events (drop out or not drop out) is using logistic regression. Unlike regular regression, the outcome calculates the predicted probability of mutually exclusive event occuring based on multiple external factors.

The equation for a logistic regression is

You may notice that logistic regressions involve the regression coefficients as a superscript to the value of *e*. This means that the coefficients have an effect on the probability. As an effect on probability, the coefficients represent odds instead of simple numerical relationships.

The fact that the coefficients represent odds ratios is particularly useful in light of the fact that the logistic regression predicts probabilities instead of a particular outcome.

## The Takeaway

Predicted probabilities are fairly straightforward. They are probabilities that are calculated from existing probabilities, though the method does depend on the nature of the probabilities involved. For example, mutually exclusive and complementary events predict probability as the product of event probabilities, the probability of dependent and complementary events has to be calculated as a sequence. Furthermore, logistic regression is a method of predicting probabilities based on more complex variable interaction, although the regression equation itself represents odds instead of traditional slope relationships.

Overall, I look forward to seeing your questions below. Happy statistics!

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