Let us take the CFA L1 exam as an example:There are 240 three-choice questions (33% probability of a correct answer for each question).Assuming a passing score of 70%, we need to get at least 240 * 70% = 168 correct answers to succeed.If we pick all Cs (in the case of a 3-choice MCQ) we can expect a score of 33%*240 = 80 but we are sure to fail (assuming correct choices of As, Bs and Cs are equally distributed), while if we choose randomly, our expected score should also be 80 but our range of results will go from 0 to 240, so we should go for this option. For each chosen number of correct answers we have a binomial distribution with a mean of np = 240 * 33% = 80 and a standard deviation of [np(1-p)]^0.5 = 7.3. Therefore, the minimum threshold of 168 is about 12 σ away from the mean which means chances of succeeding by randomly picking As, Bs or Cs are infinitesimal. a) The probability of 168 correct answers in whatever order out of 240 questions is 240! * (1/168!) * [1/(240-168)!] * (33%^168) * [(1-33%)^(240-168)].We must also account for 169 correct answers, 170, 171... until 240, and sum all those amounts.b) We can also use the Excel BINOMDIST function and calculate 1 - BINOMDIST(167, 240, 1/3, TRUE) to find the cumulative probability from 168 to 240 correct answers. We find a very small figure of order E-15 (which happens to be negative, should be positive, probably Excel cannot handle such a small figure).This is the probability to succeed in passing the CFA L1 exam by randomly choosing between As, Bs or Cs.As a conclusion, we have the choice between picking all Cs (0% success rate) and picking randomly between As, Bs and Cs (infinitesimal success rate, but infinitely better than 0%).The smart choice is the second one, and the real smart choice is to study for the exam.