This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's the solution to question 1: 1. (i) Probability of Events A and B Given: P(A' B) = (1)/(7) and P(A B) = (2)/(9). (Note: We assume the given P(A' D) is a typo and should be P(A' B).) a) Calculate P(B). The probability of event B occurring is the sum of the probabilities of (A and B) and (not A and B), since these are disjoint events that make up B. P(B) = P(A B) + P(A' B) P(B) = (2)/(9) + (1)/(7) To add these fractions, find a common denominator, which is 9 × 7 = 63. P(B) = (2 × 7)/(9 × 7) + (1 × 9)/(7 × 9) P(B) = (14)/(63) + (9)/(63) P(B) = (14 + 9)/(63) P(B) = (23)/(63) b) Calculate P(A B). The notation P(A B) typically means P(A and not B), which is P(A B'). However, with the given information, P(A B') cannot be determined as P(A) is unknown. A common alternative interpretation for in some contexts, or a possible misprint for |, is conditional probability P(A|B). We will proceed with this interpretation as it allows for a solvable problem. P(A|B) = (P(A B))/(P(B)) Using the values from the given information and part a): P(A|B) = (2)/(9)(23)/(63) P(A|B) = 29