Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A∣B), the probability of A given B.
P(A∣B) = P(A∩B)/P(B), if P(B)>0.
For example, in a deck of cards, if we know that a drawn card is a king, the probability that it is the king of hearts is:
P(King Hearts∣King) = P(King Hearts∩King)/P(King) = (1/52)/(4/52)=1/4 = 0.25.
There is a 25% chance to get the king of hearts if we know that the drawn card is a king.
In quality control, conditional probability helps in assessing the likelihood of product defects. Suppose you are a manager at a manufacturing plant, and you know that 5% of your products are defective. Additionally, if a product comes from a specific machine that has a higher defect rate, you might be interested in the probability that a randomly selected product is defective given that it comes from that machine.
- Event A: The product is defective.
- Event B: The product comes from Machine X.
If Machine X has a known defect rate, you can use this information to calculate the conditional probability.
