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?
How would you solve for these questions.. I feel that got different answers.
Thanks
1b. 1/4 = .25
Probability of both found by multiplying individual probabilities.
E. .5 * (1-.25) = ?
To solve these questions, we need to understand the number of possible outcomes and the number of favorable outcomes for each scenario.
a. The true/false question has two possible answers (true or false). Since the student is taking a random guess, there is a 1 in 2 chance of guessing the correct answer. Hence, the probability is 0.5 or 50%.
b. The multiple-choice question has four possible answers. Again, since the student is taking a random guess, there is a 1 in 4 chance of guessing the correct answer. Therefore, the probability is 0.25 or 25%.
c. To find the probability of guessing the correct answers for both questions, we multiply the probabilities of each individual event. So, the probability of guessing the correct answers to both questions is 0.5 * 0.25 = 0.125 or 12.5%.
d. Similarly, the probability of guessing the incorrect answers for both questions is also 0.5 * 0.25 = 0.125 or 12.5%.
e. To find the probability of guessing the correct answer to the true/false question and an incorrect answer to the multiple-choice question, we multiply the probability of guessing the correct answer to the true/false question with the probability of guessing an incorrect answer to the multiple-choice question. So, the probability is 0.5 * 0.75 = 0.375 or 37.5%.
f. Finally, the probability of guessing the incorrect answer to the true/false question and the correct answer to the multiple-choice question is 0.5 * 0.25 = 0.125 or 12.5%.
It's important to note that these probabilities assume that the student's guesses are truly random.
To solve these questions, we can use basic probability principles.
a. The probability of guessing the correct answer to a true/false question is 1 out of 2 chances, which is 0.5 or 50%.
b. The multiple choice question has four possible answers. Since the student is guessing, the probability of guessing the correct answer is 1 out of 4 chances, which is 0.25 or 25%.
c. To find the probability of guessing the correct answers to both questions, we multiply the probabilities of each event. So, the probability is 0.5 * 0.25 = 0.125 or 12.5%.
d. Similarly, the probability of guessing the incorrect answer to a true/false question is also 1 out of 2 chances, which is 0.5 or 50%. The probability of guessing the incorrect answer to the multiple choice question is 3 out of 4 chances, which is 0.75 or 75%. To find the probability of guessing both answers incorrectly, multiply the probabilities: 0.5 * 0.75 = 0.375 or 37.5%.
e. For this case, the probability of guessing the correct answer to the true/false question is 0.5 or 50%. The probability of guessing an incorrect answer to the multiple choice question is 3 out of 4 chances, which is 0.75 or 75%. To find the probability of guessing the correct answer to the true/false question and an incorrect answer to the multiple choice question, we multiply the probabilities: 0.5 * 0.75 = 0.375 or 37.5%.
f. The probability of guessing the incorrect answer to the true/false question is 0.5 or 50%. The probability of guessing the correct answer to the multiple choice question is 0.25 or 25%. To find the probability of guessing an incorrect answer to the true/false question and a correct answer to the multiple choice question, we multiply the probabilities: 0.5 * 0.25 = 0.125 or 12.5%.
These calculations assume that the student's guesses are completely random and independent of each other.