# Unconditional Probability.

Unconditional probability is the probability of an event occurring without any conditions being imposed on it. In other words, it is the probability of an event occurring regardless of any other events that may or may not be happening at the same time.

For example, the probability of flipping a coin and it landing on heads is 50%. This is an unconditional probability because it doesn't matter what the outcome of the previous flip was, or what the outcomes of any future flips will be. The probability is always 50% regardless of anything else. What are some key phrases used to determine conditional probabilities? The key phrases used to determine conditional probabilities are:

- if event A occurs, then event B occurs
- given that event A has occurred, event B occurs
- the probability of event B given that event A has occurred

What is the difference between conditional and unconditional mathematical expectation? The difference between conditional and unconditional mathematical expectation is that the former is calculated under the assumption that a certain event will occur, while the latter is calculated without making any assumptions about future events.

More precisely, conditional expectation is calculated as follows: first, we fix some event E and calculate the probability of this event occurring; then, we multiply this probability by the expected value of some random variable X, conditioned on the event E occurring. On the other hand, unconditional expectation is calculated by simply taking the expected value of the random variable X, without making any assumptions about future events.

Thus, the difference between the two types of expectation is that conditional expectation takes into account the probability of a certain event occurring, while unconditional expectation does not.

### What are the 4 types of probability?

There are four main types of probability, which are often referred to as the classical, empirical, subjective, and axiomatic approaches.

The classical approach is based on the work of 18th century mathematicians such as Pierre-Simon Laplace, who formulated the concept of probability based on the number of ways an event could occur divided by the total number of possible outcomes. This approach is still used in many situations, such as in gambling.

The empirical approach is based on observation and experience, rather than on theory. This approach is often used in situations where it is difficult to calculate the probability of an event occurring, such as in weather forecasting.

The subjective approach is based on the personal beliefs of the individual, rather than on any mathematical calculation. This approach is often used in situations where there is uncertainty, such as in investments.

The axiomatic approach is based on a set of axioms, or assumptions, that define what is meant by a probability. This approach is often used in theoretical or scientific settings, where it is important to be able to make deductions from a set of known facts.

##### What is conditional probability real life examples?

Conditional probability is the probability of an event occurring given that another event has already occurred.

A classic example of conditional probability is the Monty Hall problem. Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

The answer is yes. The conditional probability of winning if you switch is 2/3, whereas the probability of winning if you stick with your original choice is only 1/3.

Another example of conditional probability is the false positive rate in medical testing. Suppose a test for a certain disease is 99% accurate, that is, the probability of a positive test result if you have the disease is 0.99, and the probability of a positive test result if you don't have the disease is 0.01. If 1% of the population has the disease, what is the probability that a person who tests positive actually has the disease?

The answer is 0.99 x 0.01 = 0.0099. So even though the test is 99% accurate, if the disease is rare, the probability of a false positive is still quite high. Why Bayes theorem is used? Bayes theorem is used to update the probability of an event occurring after new information is taken into account. It is a way of revising predictions based on new data.