In high school, you learned the conditionally independent events that will happen before and after a certain event. The second event is determined by the first event!
This knowledge helps to understand how probability works, but it does not help you when there are more than two events. In these cases, you have to use the General Equation for Conditional Probability (GECCP).
The GECCP is a post-event probability that can be applied to many situations. For example, if your friend wins the lottery and they buy you a very expensive car, then the probability that they won’t buy another car is very high. What if they don’t win but someone else does? The probability they will purchase another car is still high!
This article will talk about the General Equation for Conditional Probability (GECCP), what it is, and how to use it in your personal life.
Example using the general formula for conditional probability
Say you’re walking down the street and an armed robbery breaks out nearby. You hear a gunshot and see a man run away with a bag.
The probability that someone would get robbed at this location is approximately 0.5%. If you stayed calm and didn’t worry, you could probably go about your day without much concern.
However, if you were injured or had someone stay with you while you took care of the situation, then the probability that you would be robbed went up to approximately 0.8%.
As a higher probability, your confidence in what happened increased significantly. Since we want to increase our conditional probability, we can use the general formula for conditional probability: .
Understanding the equation
The General Equation for Conditional Probability tells us how much money we can expect to win if we bet $1 on the side of probability 20-35%.
This equation can be used in several ways. One is to figure out what amount of money you should bet to increase your chance of winning!
For example, if you think you can win $25 at a gamble, then you should bet $1 per unit of money you think you can win.
Example using the conditional probability equation
If and are very small, then is nearly always . If and are large, then is almost always .
Using the General Equation for Conditional Probability, if and , the equation states that approximately half of all events occur in one of four sizes: very small, slightly small, greatly small, and very large.
Therefore, if you were to pick a banana at random, most likely you would find a medium Banana. If we were to bet $1 on whether or not the banana we picked would be small or large, we would probably choose to put our money on a small rather than a large.
If we were to put our money on one of those two chances at being small or giant, we would probably choose the smaller over the larger because of the greater expected value.
What is ?
The General Equation for Conditional Probability describes how many times you will get a certain number of outcomes, called draws, in a given set of conditions.
For example, if you are about to flip a 1-of-1 coin six times and each flip features a tail, then the General Equation for Conditional Probability describes how many times you will get a tail in your flips.
As mentioned earlier, if you are about to flip a 1-of-1 coin six times and each time the coin is heads, then the General Equation for Conditional Probability describes how many times you will get a head on your flips.
The more often an outcome occurs, the higher its probability is. This is why it is important to know what numbers have an effect on probability when playing poker.
Leave a Reply