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Conditional probability is the chance of happening a thing, given that something else has happened. It means that the probability that something will occur given that something else has occurred is equal to the probability of both things occurring divided by the probability of just one thing occurring. For example, If you think about a number between 1 and 10. Then the conditional probability that it will be an odd number would be 820 because 8 out of 20 numbers are odd. If you know what two events have happened, then you can calculate the conditional probability for each.
Probability:
Probability: It measures the likelihood that an event will occur.
It is the frequency with which a particular event happens.
Probability = Number of times event occured / Total number of possible outcomes
Conditional Probability:
Conditional Probability is the probability that an event A will occur given another event B has occurred.
The Conditional Probability formula: P(A|B) = P(A,B)/P(B)
This is the probability of event A, given event B has occurred.
Probability of a single event: It is the probability that a particular outcome from a particular set of all possible outcomes will occur. It can also be defined as the number of times an event happened divided by the total number of possible outcomes.
Calculation of conditional probability:
Calculation of conditional probability is easy to do if you know two things:
- The probability that something will occur given that something else has occurred. This is called conditional probability. If the two probabilities are different, then your calculation is wrong.
For example, take event A and another event B. The total probability is P(A) + P(B). Given that B has occurred, the probability that event A will occur is P(A|B).
- The probability of one thing occurring. If you know this, then you can figure out the conditional probability.
For example, the total probability of something happening is 5% (p = 0.05). The probability that it will happen if something else happens is 20% (p = 0.20). So P(A|B) is 0.200.05 = 4.
Importance of Conditional probability:
Conditional probability examples showing its importance in daily life:
Example 1: If you live in an area where it’s very likely that a hurricane will hit you, then the probability that a tropical storm will make landfall is much higher if it’s in the Caribbean or Atlantic than if it’s in the Pacific. This means you should calculate your chances differently depending on the location of a tropical storm.
Example 2: When you’re making a decision, it’s important to understand the probability that something will occur if you choose something and that something will occur if you choose another. For instance, some people don’t want to buy things because they are worried about their credit score. This means that they feel more likely than not that their score will decrease if they buy things on credit.
Example 3: You’re thinking about buying a lottery ticket, but before you do, you want to know how likely you’ll win versus how likely it is that you won’t win. So if the probability of winning is greater than the probability of not winning, then buying a lottery ticket makes sense.
Uses of conditional probability:
Conditional probability can be used to determine the probability of an event happening, given that some other event has occurred. Conditional probability is particularly useful in statistics when applied to questions related to data collected in the past.
For example, suppose a new medication is being developed. In that case, researchers will analyse the past medication data to determine which patients are more likely to benefit from the new medication. They can then use this to predict better which patients might benefit from the new medication and how likely they are to benefit.
Conditional probability is also useful when we want to determine how likely two events will happen together, given that they did not happen (or the exact opposite). For example, suppose we know that a particular person has been diagnosed with lung cancer, and we want to find out how likely they will die within two years. In that case, it is useful to use conditional probability.
Conclusion:
Conditional probability is one of the most widely used techniques in statistics to analyze the probability of an event, given that another event has occurred. There are many different ways that conditional probability can be used. Predictive models with data from the past can be used to predict the future. Knowing a lot about the past data when a new problem arises can help us predict what will happen in the future. For example, we know that if an individual has received a diagnosis of breast cancer in the past, then it is very likely that they will get it again.
