Standard Tests Standard tests, such as the SAT or ACT or MCAT,...

Question

Standard Tests Standard tests, such as the SAT or ACT or MCAT, tend to make extensive use of multiple-choice questions because they are easy to grade using software. If one such multiple choice question has possible correct answers of a, b, c, d, e, what is the probability of a wrong answer if the answer is a random guess?

Accepted Answer

Welcome back, everyone. A digital door lock asks the user to select the correct access code from 5 options labeled P, Q, R, S, and C. If someone tries to unlock the door by randomly choosing one of the five options, what is the probability that they enter the wrong code? A says 0.2, B 0.7, C 0.8, and D 0.4. So for this problem, let's define an event A, which represents entering the wrong code. We want to identify the probability of a, and for this problem we're going to use the method of complements. The probability of a wrong code is equal to 1 minus the probability of the complement of a, meaning entering the correct code. So we want to identify the probability of entering the correct code, and that's E of a bar, right? So now we have 5 options P, Q, R, S, and C. So the total number of outcomes which goes into the denominator is 5 and only one of them is correct, for example, Q. So the probability of getting a correct code is 1/5. And now we're going to substitute it into the previous equation which gives us the probability of the wrong code, and that's 1 minus 15th, which is 4/5s or when divided 0.8. Meaning the correct answer to this problem corresponds to the answer to a C. Thank you for watching.

��app

Key Concepts

Probability

Complementary Events

Random Guessing

Watch next