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 to the problems: Question 15: Step 1: List all possible outcomes when a fair coin is tossed 3 times. The total number of outcomes is 2^3 = 8. The outcomes are: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. Step 2: Identify the outcomes with at least two heads. "At least two heads" means two heads or three heads. The favorable outcomes are: HHH, HHT, HTH, THH. There are 4 favorable outcomes. Step 3: Calculate the probability. P(at least two heads) = Number of favorable outcomesTotal number of outcomes P(at least two heads) = (4)/(8) Step 4: Simplify the probability. P(at least two heads) = (1)/(2) The correct option is D. D. (1)/(2) Question 16: Step 1: Determine the total number of outcomes when two fair dice are rolled. Each die has 6 faces, so for two dice, the total number of outcomes is 6 × 6 = 36. Step 2: Identify the outcomes where both dice show the same number. The favorable outcomes are: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). There are 6 favorable outcomes. Step 3: Calculate the probability. P(same number) = Number of favorable outcomesTotal number of outcomes P(same number) = (6)/(36) Step 4: Simplify the probability. P(same number) = (1)/(6) The correct option is C. C. (1)/(6) Question 17: Step 1: List all possible outcomes when two fair coins are tossed. The total number of outcomes is 2^2 = 4. The outcomes are: HH, HT, TH, TT. Step 2: Identify the outcomes with at least one head. "At least one head" means one head or two heads. The favorable outcomes are: HH, HT, TH. There are 3 favorable outcomes. Step 3: Calculate the probability. P(at least one head) = Number of favorable outcomesTotal number of outcomes P(at least one head) = (3)/(4) The correct option is D. D. (3)/(4) Question 18: Step 1: Determine the total number of outcomes when two dice are thrown together. The total number of outcomes is 6 × 6 = 36. Step 2: Identify the outcomes where the sum of the numbers is 10. The favorable outcomes are: (4,6), (5,5), (6,4). There are 3 favorable outcomes. Step 3: Calculate the probability. P(sum of 10) = Number of favorable outcomesTotal number of outcomes P(sum of 10) = (3)/(36) Step 4: Simplify the probability. P(sum of 10) = (1)/(12) The correct option is B. B. (1)/(12) Question 19: Step 1: Determine the probability of the top face being white on a single throw. A die has 6 faces. 4 faces are white. P(White on one throw) = Number of white facesTotal number of faces = (4)/(6) Step 2: Simplify the probability for a single throw. P(White on one throw) = (2)/(3) Step 3: Calculate the probability of the top face being white in two consecutive throws. Since the throws are independent events, multiply the probabilities. P(White in both cases) = P(White on 1st throw) × P(White on 2nd throw) P(White in both cases) = (2)/(3) × (2)/(3) Step 4: Calculate the final probability. P(White in both cases) = (4)/(9) The correct option is C. C. (4)/(9) Send me the next one 📸