# Conditional Probability

## Conditional Probability :

Conditional probability is the probability of an event occurring given that another event has already occurred. For example, let’s say we have a bag with 10 red balls and 5 blue balls. The probability of picking a red ball from the bag without looking is 10/15 or 2/3. However, if we know that the first ball we picked from the bag was blue, the probability of picking a red ball on the second pick changes. This is because there are now only 4 balls left in the bag, and only 4 of them are red. So the probability of picking a red ball on the second pick, given that the first ball was blue, is 4/9.
Another example of conditional probability is in the field of medical testing. Let’s say a certain disease is relatively rare, occurring in only 1% of the population. A test for the disease is 99% accurate, meaning that 99% of the time it correctly identifies whether a person has the disease or not. However, the probability of a positive test result can be different depending on the person’s overall likelihood of having the disease. For example, if a person has no symptoms and no family history of the disease, the probability of them having the disease is very low, so the probability of a positive test result, given that they do not have the disease, is also very low. However, if a person has symptoms and a family history of the disease, the probability of them having the disease is much higher, so the probability of a positive test result, given that they do have the disease, is also much higher.
In summary, conditional probability is the probability of an event occurring given that another event has already occurred. It is important to consider the context and all available information when calculating the probability of an event.