A QUESTION ON A PROFICIENCY TEST IS MULTIPLE CHOICE WITH 4 POSSIBLE ANSWERS, 1 OF WHICH IS CORRECT. ASSUMING THAT ALL RESPONSES ARE RANDOM GUESSES FIND THE PROBABILITY THAT AMOUNG 12 TEST SUBJECTS, EXACTLY 5 ANSWERS ARE CORRECT

In this scenario, there are only 2 possible outcomes. It is either the answer is correct or wrong.Since the outcomes are independent, it means that it is binomial probability. We would apply the binomial distribution formula which is expressed asP(x) = nCx * p^x * q^(n - x)wheren is the sample sizex is the number of successesp is the probability of successq = 1 - p = probability of failureFrom the information given, p = 1/4 = 0.25q = 1 - 1/4 = 3/4 = 0.75n = 12x = 5We want to find P(x = 5)P(x = 5) = 12C5 * 0.25^5 * 0.75^(12 - 5)P(x = 5) = 0.103The probability that among 12 test subjects, exactly 5 answers are correct is 0.103l