Question

A news magazine publishes three columns entitled"Art(A)" "Book(B)" "Cinema(C)". Read ing habits of a randomly selected reader wit h respect to these columns are: Find P(A∣B∪C) and P(A∪B∣C), respectivel y.

Answer 1

The question seeks to calculate conditional and combined probabilities in mathematics. Probability rules like the multiplication and addition rule are applicable, yet additional information about the independent probabilities and overlaps between the events A, B, and C is required for precise calculations.

Step-by-step explanation:

The question involves calculating conditional and combined probabilities, which is within the domain of mathematics, more specifically probability theory. To find P(A∖B) and P(A⊂B∪C), we need additional information such as the individual probabilities and any overlaps between events A, B, and C. However, using the given examples and probability rules, we can understand the concepts behind the calculations.

For instance, the multiplication rule states that if events A and B are independent, then the probability of both A and B occurring is the product of their individual probabilities: P(A AND B) = P(A) × P(B). If events are mutually exclusive, it means they cannot occur together, so the probability of both A and B occurring is zero: P(A AND B) = 0.

Similarly, the addition rule provides a way to compute the probability of either event A or event B occurring: P(A OR B) = P(A) + P(B) - P(A AND B). This formula subtracts the overlap because adding individual probabilities counts the overlap twice.