1. A student taking a midterm exam in Ancient History comes to two questions pertaining to a lecture that he missed, and so he decides to take a random guess on both questions. One question is true-false and the other is multiple choice with four possible answers. What is the probability of guessing?
a. the correct answer to the true/false question? – 1 out of 2 chances – 0.5 or 50%
b. the correct answer to the multiple choice question?
c. the correct answers to both the true/false question and the multiple choice question?
d. the incorrect answers to both the true/false question and the multiple choice question?
e. the correct answer to the true/false question and an incorrect answer to the multiple choice question?
f. the incorrect answer to the true/false question and the correct answer to the multiple choice question?
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b. the correct answer to the multiple choice question? - 1 out of 4 chances - 0.25 or 25%
c. the correct answers to both the true/false question and the multiple choice question? - The probability of both events occurring is the product of their individual probabilities. So, 0.5 (for the true/false question) multiplied by 0.25 (for the multiple choice question) equals 0.125 or 12.5%.
d. the incorrect answers to both the true/false question and the multiple-choice question? - The probability of guessing an incorrect answer to the true/false question is 0.5, and the probability of guessing an incorrect answer to the multiple-choice question is 0.75 (since there are 3 incorrect choices out of 4). To calculate the probability of both events occurring, multiply these probabilities: 0.5 multiplied by 0.75 equals 0.375 or 37.5%.
e. the correct answer to the true/false question and an incorrect answer to the multiple-choice question? - The probability of guessing the correct answer to the true/false question is 0.5, and the probability of guessing an incorrect answer to the multiple-choice question is 0.75. To calculate the probability of both events occurring, multiply these probabilities: 0.5 multiplied by 0.75 equals 0.375 or 37.5%.
f. the incorrect answer to the true/false question and the correct answer to the multiple-choice question? - The probability of guessing an incorrect answer to the true/false question is 0.5, and the probability of guessing the correct answer to the multiple-choice question is 0.25. To calculate the probability of both events occurring, multiply these probabilities: 0.5 multiplied by 0.25 equals 0.125 or 12.5%.
To calculate the probability of guessing, we need to know the number of possible outcomes and the number of favorable outcomes.
a. For the true/false question, there are only two possible outcomes: true or false. Since the student is taking a random guess, there is a 50% chance of guessing the correct answer.
b. For the multiple choice question with four possible answers, there is a 25% chance of guessing the correct answer, or 1 out of 4 chances.
c. To find the probability of guessing both questions correctly, we multiply the individual probabilities. So, the probability would be 0.5 * 0.25 = 0.125 or 12.5%.
d. To find the probability of guessing both questions incorrectly, we subtract the probability of getting both questions correct from 1. Thus, the probability would be 1 - 0.125 = 0.875 or 87.5%.
e. To find the probability of guessing the true/false question correctly and the multiple-choice question incorrectly, we multiply the individual probabilities. So, the probability would be 0.5 * 0.75 = 0.375 or 37.5%.
f. To find the probability of guessing the true/false question incorrectly and the multiple-choice question correctly, we multiply the individual probabilities. So, the probability would be 0.5 * 0.25 = 0.125 or 12.5%.