The formula for calculating conditional probability is P(A/B) = P(A ∩ B) / P(B), where P(A/B) represents the probability of event A occurring given that event B has already occurred.
P(A) represents the probability of event A occurring, P(A U B) represents the probability of either event A or event B occurring, and P(A ∩ B) represents the probability of both event A and event B occurring.
To find P(A/B), we can use the formula P(A/B) = P(A ∩ B) / P(B). In this case, P(B) can be calculated by subtracting P(A ∩ B) from P(A U B), as P(A U B) represents the probability of either event A or event B occurring. Therefore, P(B) = P(A U B) - P(A ∩ B). Substituting this value into the formula, we get P(A/B) = (P(A ∩ B) / (P(A U B) - P(A ∩ B)).
To find the value of P(A/B), we can substitute the given values into the formula P(A/B) = (P(A ∩ B) / (P(A U B) - P(A ∩ B)). In this case, P(A ∩ B) = 0.1, P(A U B) = 0.8, and P(A) = 0.5. Therefore, P(A/B) = (0.1 / (0.8 - 0.1)) = 0.125.
The value of P(A/B) represents the probability of event A occurring given that event B has already occurred. In other words, it represents the likelihood of event A happening in a sample space where event B has already occurred. In this case, P(A/B) = 0.125 means that there is a 12.5% chance of event A occurring in a sample space where event B has already occurred.