a student took a 25 question true and false test answering the question randomly without reading them. If a score of 18 is correct is the minimum passing grade, how likely (calculate probability) is it that the random guesser will pass the test
To calculate the probability of the random guesser passing the test, we need to determine the number of correct answers they are expected to get by chance.
In a true or false test with 2 possible choices (true or false), there is a 50% chance of guessing the correct answer for each question. Therefore, on average, the random guesser is expected to get half of the questions correct by chance.
Out of the 25 questions, if the random guesser is expected to get half correct, that would be 25 * 0.5 = 12.5 questions, which cannot be our final answer since we can't have half a question correct.
Since we cannot have a fraction of a correct answer, we need to round up or down. In this case, we'll assume that rounding up would be more favorable for the student, so we'll consider this 12 correct answers.
To pass the test, the student needs to get at least 18 correct answers. Since it is not possible for the random guesser to get more than 12 correct answers, the probability of the random guesser passing the test is 0.
Thus, it is impossible for the random guesser to pass the test based on their random guessing strategy alone.