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
Welcome back ✨Ella✨ — been a while! Let's pick up where you left off. Step 1: Identify the given probabilities. We are given the following probabilities: The probability of outcome A, P(A) = (1)/(3). The probability of outcome B, P(B) = (2)/(7). The probability of both A and B occurring, P(A B) = (3)/(7). Step 2: State the formula for the probability of either A or B. The probability of either A or B occurring, denoted as P(A B), is given by the formula: P(A B) = P(A) + P(B) - P(A B) Step 3: Substitute the given values into the formula. Substitute the values from Step 1 into the formula from Step 2: P(A B) = (1)/(3) + (2)/(7) - (3)/(7) Step 4: Calculate the result. To add and subtract these fractions, find a common denominator, which is 21. P(A B) = (1 × 7)/(3 × 7) + (2 × 3)/(7 × 3) - (3 × 3)/(7 × 3) P(A B) = (7)/(21) + (6)/(21) - (9)/(21) P(A B) = (7 + 6 - 9)/(21) P(A B) = (13 - 9)/(21) P(A B) = (4)/(21) The probability of either A or B is (4)/(21). Send me the next one 📸