a) What is the probability of getting heads on onlyone of your flips?
The cases favorable to the event E1 of getting heads on only one of your flips are,
E1 = {(HTT), (TTH), (THT)}
n (E1) = 3
P (E1) = n (E1) / n (S) = 3/8 = 0.375
(b) What is the probability of getting heads on at least one flip? The cases favorable to the event E2 of getting heads on only one of your flips are,
E2 = {(HHH), (HHT), (HTH), (THH), (HTT), (TTH), (THT)}
n (E2) = 7
P (E2) = n (E2) / n (S) = 7/8 = 0.875
2. You are to participate in an exam for which you had no chance to study, and for that reason cannot do anything but guess for each question (all questions being of the multiple choice type, so the chance of guessing the correct answer for each question is 1/d, d being the number of options (distractors) per question; so in case of a 4-choice question, your guess chance is 0.25). Your instructor offers you the opportunity to choose amongst the following exam formats: I. 6 questions of the 4-choice type; you pass when 5 or more answers are correct; II. 5 questions of the 5-choice type; you pass when 4 or more answers are correct; III. 4 questions of the 10-choice type; you pass when 3 or more answers are correct. Rank the three exam formats according to their attractiveness. It should be clear that the format with the highest probability to pass is the most attractive format. Which would you choose and why?