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
To find the probability that Lorenzo will get at least one correct answer, we can use the complement rule. The probability of getting at least one correct answer is equal to 1 minus the probability of getting zero correct answers (i.e., all answers incorrect). Step 1: Determine the probability of getting a single question correct and incorrect. There are four options for each question, and only one is correct. The probability of getting a question correct is P(correct) = (1)/(4) = 0.25. The probability of getting a question incorrect is P(incorrect) = 1 - P(correct) = 1 - (1)/(4) = (3)/(4) = 0.75. Step 2: Calculate the probability of getting all five questions incorrect. Since there are five questions and each is independent, the probability of getting all five incorrect is: P(all incorrect) = (P(incorrect))^5 P(all incorrect) = ((3)/(4))^5 P(all incorrect) = (0.75)^5 P(all incorrect) = 0.75 × 0.75 × 0.75 × 0.75 × 0.75 P(all incorrect) = 0.2373046875 Step 3: Calculate the probability of getting at least one correct answer. Using the complement rule: P(at least one correct) = 1 - P(all incorrect) P(at least one correct) = 1 - 0.2373046875 P(at least one correct) = 0.7626953125 Step 4: Round the probability to three decimal places and select the corresponding option. Rounding 0.7626953125 to three decimal places gives 0.763. This matches option C. The final answer is C. 0.763. That's 2 down. 3 left today — send the next one.