Assumption: The probability that Forson will pass the examination is (3)/(4), as the image cuts off the last fraction.

Here is the solution to your question. Assumption: The probability that Forson will pass the examination is (3)/(4), as the image cuts off the last fraction. Part 9(a): Probability Let P(A), P(I), and P(F) be the probabilities that Ayuba, Idris, and Forson pass the examination, respectively. Given: P(A) = (2)/(3) P(I) = (5)/(8) P(F) = (3)/(4) The probabilities that they fail are: P(A') = 1 - P(A) = 1 - (2)/(3) = (1)/(3) P(I') = 1 - P(I) = 1 - (5)/(8) = (3)/(8) P(F') = 1 - P(F) = 1 - (3)/(4) = (1)/(4) i. The three of them will pass the examination Step 1: Multiply the individual probabilities of passing. P(A and I and F pass) = P(A) × P(I) × P(F) P(A and I and F pass) = (2)/(3) × (5)/(8) × (3)/(4) Step 2: Calculate the product. P(A and I and F pass) = (2 × 5 × 3)/(3 × 8 × 4) = (30)/(96) Step 3: Simplify the fraction. P(A and I and F pass) = (5)/(16) The probability that the three of them will pass is (5)/(16). ii. None of them will pass the examination Step 1: Multiply the individual probabilities of failing. P(None pass) = P(A') × P(I') × P(F') P(None pass) = (1)/(3) × (3)/(8) × (1)/(4) Step 2: Calculate the product. P(None pass) = (1 × 3 × 1)/(3 × 8 × 4) = (3)/(96) Step 3: Simplify the fraction. P(None pass) = (1)/(32) The probability that none of them will pass is (1)/(32). iii. Ayuba and Idris will pass the examination Step 1: Multiply the probabilities of Ayuba and Idris passing. P(A and I pass) = P(A) × P(I) P(A and I pass) = (2)/(3) × (5)/(8) Step 2: Calculate the product. P(A and I pass) = (10)/(24) Step 3: Simplify the fraction. P(A and I pass) = (5)/(12) The probability that Ayuba and Idris will pass is (5)/(12). Part 9(b): Ratio Problem Step 1: Find the initial number of boys and girls. Total students = 432 Ratio of boys to girls = 5:4 Total ratio parts = 5 + 4 = 9 Initial number of boys: B_initial = (5)/(9) × 432 = 5 × 48 = 240 Initial number of girls: G_initial = (4)/(9) × 432 = 4 × 48 = 192 Step 2: Calculate the new number of boys. The number of boys increases by 12. B_new = B_initial + 12 = 240 + 12 = 252 Step 3: Use the new ratio to find the new number of girls. The new ratio of boys to girls is 7:6. B_newG_new = (7)/(6) (252)/(G_new) = (7)/(6) G_new = (252 × 6)/(7) G_new = 36 × 6 = 216 Step 4: Find the increase in the number of girls. Increase in girls = G_new - G_initial Increase in girls = 216 - 192 = 24 The increase in the number of girls is 24. Send me the next one 📸