# Basic Basics of Statistics(Descriptive) & Probability for Data Scientists-A Quick Refresher

Probability deals with predicting the likelihood of future events, while statistics involves the analysis of the frequency of past events.

# PROBABILITY

In probability theory, an event is a set of outcomes of an experiment to which a probability is assigned. If `E` represents an event, then `P(E)` represents the probability that `E`will occur. A situation where `E` might happen (success) or might not happen (failure) is called a trial.

This event can be anything like tossing a coin, rolling a die or pulling a colored ball out of a bag. In these examples the outcome of the event is random, so the variable that represents the outcome of these events is called a random variable.

The empirical probability of an event is given by number of times the event occurs divided by the total number of incidents observed. If for`n`trials and we observe `s`successes, the probability of success is s/n.

Theoretical probability on the other hand is given by the number of ways the particular event can occur divided by the total number of possible outcomes.

## JOINT AND CONDITIONAL PROBABILITY

Joint Probability: Probability of events A and B denoted by`P(A and B) or P(A ∩ B)`is the probability that events A and B both occur.

`P(A ∩ B) = P(A). P(B)` . This only applies if `A`and `B`are independent, which means that if `A`occurred, that doesn’t change the probability of `B`, and vice versa.

Conditional Probability: When A and B are not independent, it is useful to compute the conditional probability, P (A|B), which is the probability of A given that B occurred: `P(A|B) = P(A ∩ B)/ P(B)`.

The probability of an event A conditioned on an event B is denoted and defined `P(A|B) = P(A∩B)/P(B)`

Similarly, `P(B|A) = P(A ∩ B)/ P(A)` . We can write the joint probability of as A and B as `P(A ∩ B)= p(A).P(B|A)`, which means : “The chance of both things happening is the chance that the first one happens, and then the second one given the first happened.”