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
Step 1: Identify the given probabilities. Let P(M) be the probability that Mensah passes Mathematics. Let P(E) be the probability that Mensah passes Economics. Let P(M E) be the probability that Mensah passes at least one subject. We are given: P(M) = (3)/(4) P(E) = (5)/(8) P(M E) = (7)/(12) Step 2: State the formula for the probability of the union of two events. The formula for the probability of the union of two events is: P(M E) = P(M) + P(E) - P(M E) where P(M E) is the probability that Mensah passes both subjects. Step 3: Rearrange the formula to solve for P(M E). P(M E) = P(M) + P(E) - P(M E) Step 4: Substitute the given values into the formula. P(M E) = (3)/(4) + (5)/(8) - (7)/(12) Step 5: Find a common denominator for the fractions and perform the calculation. The least common multiple (LCM) of 4, 8, and 12 is 24. Convert each fraction to have a denominator of 24: (3)/(4) = (3 × 6)/(4 × 6) = (18)/(24) (5)/(8) = (5 × 3)/(8 × 3) = (15)/(24) (7)/(12) = (7 × 2)/(12 × 2) = (14)/(24) Now substitute these equivalent fractions back into the equation: P(M E) = (18)/(24) + (15)/(24) - (14)/(24) P(M E) = (18 + 15 - 14)/(24) P(M E) = (33 - 14)/(24) P(M E) = (19)/(24) The probability that Mensah passes both subjects is (19)/(24). The final answer is (19)/(24).