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 Jedidah🎀 — missed you this week. Here are the solutions to the probability questions: 8. Step 1: Understand the relationship between an event and its complement. The probability of an event happening plus the probability of the event not happening is equal to 1. Let P(late) be the probability that a boy will be late for school, and P(not late) be the probability that he will not be late for school. We are given P(late) = x. Step 2: Use the complementary probability formula. P(late) + P(not late) = 1 x + P(not late) = 1 Step 3: Solve for P(not late). P(not late) = 1 - x The probability that he will not be late for school is 1 - x. 9. Step 1: Identify the given probability and the event whose probability is required. The probability of Kasukulu waking up late is 0.3. We need to find the probability that she will wake up early. Waking up early is the complement of waking up late in this context. Let P(late) be the probability of waking up late, and P(early) be the probability of waking up early. We are given P(late) = 0.3. Step 2: Apply the complementary probability formula. P(late) + P(early) = 1 0.3 + P(early) = 1 Step 3: Calculate P(early). P(early) = 1 - 0.3 P(early) = 0.7 The probability that she will wake up early is 0.7. 10. Step 1: Identify the given probability and the event whose probability is required. The probability of getting a black button is (2)/(9). We need to find the probability of getting a button which is not black. "Not black" is the complement of "black". Let P(black) be the probability of getting a black button, and P(not black) be the probability of getting a button that is not black. We are given P(black) = (2)/(9). Step 2: Apply the complementary probability formula. P(black) + P(not black) = 1 (2)/(9) + P(not black) = 1 Step 3: Calculate P(not black). P(not black) = 1 - (2)/(9) P(not black) = (9)/(9) - (2)/(9) P(not black) = (7)/(9) The probability of getting a button which is not black is (7)/(9). Send me the next one 📸