# Conditional and joint probabilities of statistically dependent events

• I
• PainterGuy
In summary, the formulas for calculating conditional and joint probability are dependent on each other. One cannot be calculated without the other, leading to a potential problem. It is necessary to know either the conditional or joint probability in order to calculate the other, and the independence of the two cannot be determined without this information.
PainterGuy
Hi,

If the events A and B are statically dependent then the following formulas are used to calculate conditional probability and joint probability but there is a problem. As I see it both formulas are dependent upon each other. One cannot calculate conditional probability without first calculating joint probability, and one cannot calculate joint probability without knowing condition probability! Where am I going wrong? Could you please help me? Thank you!

PainterGuy said:
As I see it both formulas are dependent upon each other. One cannot calculate conditional probability without first calculating joint probability, and one cannot calculate joint probability without knowing condition probability! Where am I going wrong? Could you please help me?
Well, you have to know something. If you know the conditional probability then you can calculate the joint probability. If you know the joint probability then you can calculate the conditional probability. If you don't know either then you cannot even tell if they are independent or not.

pbuk, PainterGuy and FactChecker

## 1. What is conditional probability?

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is calculated by dividing the probability of the two events occurring together by the probability of the first event occurring.

## 2. How is conditional probability different from joint probability?

Conditional probability focuses on the likelihood of an event occurring given that another event has already occurred, while joint probability looks at the likelihood of two events occurring together.

## 3. How do you calculate conditional probability?

Conditional probability is calculated by dividing the joint probability of two events by the probability of the first event occurring.

## 4. What is the relationship between conditional and independent events?

If two events are independent, then the occurrence of one event does not affect the probability of the other event occurring. In this case, the conditional probability would be equal to the joint probability. However, if the events are dependent, the conditional probability will be different from the joint probability.

## 5. Can you give an example of conditional and joint probabilities of statistically dependent events?

One example could be the probability of a student passing a test given that they have studied for it. This would be the conditional probability. The joint probability would be the likelihood of the student passing the test and studying for it. These events are dependent because the student's likelihood of passing the test is influenced by whether or not they have studied for it.

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