A quiz consists of 90 multiple-choice questions, each with 4 possible answers (A, B, C and D). For someone who makes random guess , A is the correct answer for all the questions. If each right answer carries 4 marks and each wrong answer gives -1/4 marks, what probable marks someone will get?
222.5 + probable marks
how?
To determine the probable marks someone will get for making random guesses, we need to calculate the expected value.
The first step is to determine the probability of getting the correct answer for each question. Since there are 4 possible answers and one of them is correct (A), the probability of randomly guessing the right answer is 1/4.
Next, we calculate the expected value for each question. Each correct answer gives 4 marks, while each wrong answer gives -1/4 marks. So, the expected value for each question is:
Expected value = (Probability of correct answer * Marks for correct answer) + (Probability of wrong answer * Marks for wrong answer)
= (1/4 * 4) + (3/4 * (-1/4))
= 1 + (-3/16)
= 13/16
Now, we can calculate the total probable marks by multiplying the expected value of each question by the total number of questions:
Total probable marks = Expected value * Total number of questions
= (13/16) * 90
= 58.125
Hence, the probable marks someone will get for making random guesses in this scenario is approximately 58.125 marks.