Conditional Probability
Conditional Probability
In real life, we often come across situations where the outcome of one event affects the probability of another. For example, if we know it is cloudy, the chance of rain increases. This type of probability is called conditional probability. It is the probability of an event happening given that another event has already occurred.
What is Conditional Probability?
Conditional probability is the probability of an event occurring, assuming that another event has already taken place. It helps in narrowing down the sample space and focusing only on the outcomes that are relevant under the given condition.
We denote the conditional probability of event A occurring given that event B has occurred as: P(A|B).
Mathematical Formula
The formula to calculate conditional probability is:
P(A|B) = P(A ∩ B) / P(B), where P(B) ≠ 0
Here,
- P(A|B) is the probability of event A given that B has occurred
- P(A ∩ B) is the probability that both events A and B occur
- P(B) is the probability that event B occurs
Uses of Conditional Probability
Some of the uses are as follows:
- In weather forecasting, to predict rain given cloud coverage
- In medical testing to determine the probability of a disease given symptoms
- In finance, to assess risk given certain market conditions
- In machine learning for building probabilistic models
- In games and puzzles where outcomes depend on prior events
Basic Example
Suppose we have a deck of 52 playing cards. What is the probability of drawing a Queen given that the card drawn is a face card?
Total face cards (J, Q, K) in a deck = 12
Total Queens in the face cards = 4
So, the conditional probability is:
P(Queen | Face card) = Number of Queens / Number of Face cards = 4 / 12 = 1 / 3
Bayes Theorem
https://www.testingdocs.com/bayes-theorem-in-probability-theory/
