Final answer:
P(A/B) = 0.50
Explanation:
To find the probability of A given that B has occurred, we use the formula P(A/B) = P(A∩B) / P(B), where P(A∩B) represents the probability of A and B both occurring. In this case, since A and B are independent events, the probability of A and B both occurring is simply the product of their individual probabilities, which gives us P(A/B) = P(A) * P(B) = 0.50 * 0.20 = 0.10. This means that there is a 10% chance that event A will occur given that event B has already occurred.
Now, let's dive deeper into the explanation for a better understanding. When two events are independent, it means that the occurrence of one event does not affect the probability of the other event. In other words, the outcome of one event has no influence on the outcome of the other event. In this scenario, event A and event B are independent, which means that the probability of A occurring remains the same whether or not event B has occurred.
To find the probability of A given that B has occurred, we need to look at the probability of both events happening together, i.e., A and B both occurring. This is represented as P(A∩B) and can be calculated by multiplying the individual probabilities of A and B, which gives us P(A∩B) = P(A) * P(B). In this case, P(A) = 0.50 and P(B) = 0.20, which gives us P(A∩B) = 0.50 * 0.20 = 0.10.
Next, we need to divide P(A∩B) by P(B) to get the probability of A given that B has occurred. This gives us P(A/B) = P(A∩B) / P(B) = 0.10 / 0.20 = 0.50. This means that there is a 50% chance of event A occurring given that event B has already occurred.
In conclusion, the probability of A given that B has occurred is 0.50 or 50%. This means that the outcome of event B has no impact on the outcome of event A and the probability of A remains the same regardless of whether event B has occurred or not. This can also be seen in the formula, where P(A/B) = P(A) * P(B), as P(B) is a constant factor and has no effect on the value of P(A/B).
In summary, the probability of A given that B has occurred is 0.50 or 50%, and this is due to the independence of both events. The formula P(A/B) = P(A) * P(B) can be used to find the probability of A given that B has occurred, where P(A) and P(B) represent the individual probabilities of A and B. It is important to note that this formula only applies to independent events, as the occurrence of one event does not affect the probability of the other event. Therefore, P(A/B) remains the same regardless of whether event B has occurred or not.