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.
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Here are the solutions for questions 5 and 6. Question 5: Probability of Musa and Okeke passing mathematics tests. Given probabilities: P(Musa passes) = P(M) = 0.75 P(Okeke passes) = P(O) = 0.4 From these, we can find the probabilities of them failing: P(Musa fails) = P(M') = 1 - P(M) = 1 - 0.75 = 0.25 P(Okeke fails) = P(O') = 1 - P(O) = 1 - 0.4 = 0.6 a) Draw a tree diagram to illustrate the outcomes of the two independent events. ` Start ├── Musa Passes (P=0.75) │ ├── Okeke Passes (P=0.4) -> Outcome: (M, O), P = 0.75 * 0.4 = 0.30 │ └── Okeke Fails (P=0.6) -> Outcome: (M, O'), P = 0.75 * 0.6 = 0.45 └── Musa Fails (P=0.25) ├── Okeke Passes (P=0.4) -> Outcome: (M', O), P = 0.25 * 0.4 = 0.10 └── Okeke Fails (P=0.6) -> Outcome: (M', O'), P = 0.25 * 0.6 = 0.15 ` b) Calculate the probabilities that: (i) both of them will pass the test Step 1: Identify the event. This means Musa passes AND Okeke passes. Since the events are independent, we multiply their probabilities. P(both pass) = P(M) × P(O) Step 2: Substitute values and calculate. P(both pass) = 0.75 × 0.4 P(both pass) = 0.30 The probability that both of them will pass the test is 0.30. (ii) both of them will fail the test Step 1: Identify the event. This means Musa fails AND Okeke fails. Since the events are independent, we multiply their probabilities of failing. P(both fail) = P(M') × P(O') Step 2: Substitute values and calculate. P(both fail) = 0.25 × 0.6 P(both fail) = 0.15 The probability that both of them will fail the test is 0.15. (iii) only one of them will pass the test Step 1: Identify the events. This can happen in two ways: (Musa passes AND Okeke fails) OR (Musa fails AND Okeke passes). We calculate the probability of each case and add them. P(only one passes) = (P(M) × P(O')) + (P(M') × P(O)) Step 2: Substitute values and calculate. P(only one passes) = (0.75 × 0.6) + (0.25 × 0.4) P(only one passes) = 0.45 + 0.10 P(only one passes) = 0.55 The probability that only one of them will pass the test is 0.55. Question 6: Survey on favourite soft drinks. The table shows the number of students who prefer each drink: • Coke: 20 students • Fanta: 15 students • Sprite: 10 students • Lemon: 5 students a) How many students are involved in the survey? Step 1: Sum the number of students for each drink. The total number of students is the sum of all the numbers in the "Numbers" row. Total students = 20 + 15 + 10 + 5 Step 2: Calculate the total. Total students = 50 The total number of students involved in the survey is 50. Got more? Send 'em.