What is conditional probability formula?

The conditional probability formula is P(A|B) = P(A and B) / P(B), where A and B are events.

Conditional probability is the probability of an event A occurring given that event B has already occurred. The formula for conditional probability is P(A|B) = P(A and B) / P(B), where A and B are events.

P(A and B) represents the probability of both events A and B occurring together. P(B) represents the probability of event B occurring. By dividing the probability of both events occurring together by the probability of event B occurring, we get the probability of event A occurring given that event B has already occurred.

For example, let's say we have a bag of 10 marbles, 6 of which are red and 4 of which are blue. If we randomly select one marble from the bag, the probability of selecting a red marble is 6/10 or 0.6. Now, let's say we randomly select a marble from the bag and it is blue. What is the probability that the next marble we select will be red?

Using the conditional probability formula, we have P(Red|Blue) = P(Red and Blue) / P(Blue). The probability of selecting a blue marble is 4/10 or 0.4. If we assume that we do not replace the blue marble back into the bag, the probability of selecting a red marble after selecting a blue marble is 6/9 or 0.67. Therefore, P(Red|Blue) = (4/10) * (6/9) = 0.267.

In summary, the conditional probability formula is used to calculate the probability of an event occurring given that another event has already occurred. It is a useful tool in many areas of mathematics and statistics.