Basic Counting Problems 1. Matthew Mattox, a student enrolled in Applied Stat, i
ID: 3272676 • Letter: B
Question
Basic Counting Problems 1. Matthew Mattox, a student enrolled in Applied Stat, is taking a pop quiz. There are three multiple choice questions, each with five possible answers. How many possible ways can the answer form for this quiz be completed? Assume that Matthew will select one answer per question. 2. This is Matthew's unlucky day. He also gets a pop quiz in Abstract Alg Abstract quiz consists of three True-False questions, followed by one multiple choice question with four possible answers. How many possible ways can the answer form for this quiz be completed? Assume that Matthew will select one answer per question Suppose Matthew is totally clueless on both of these quizzes and is therefore relegated to randomly guessing. What is the probability that he will make a perfect score on the Applied Stat quiz? What about the Abstract quiz? 3. 4 An unorganized professor has five unmarked flash drives in his desk. Here is what is actually stored on these flash drives, which we will refer to as flash drives A, B, C, D,. A: Old Applied Stat exams B: Old Experimental Design exams C: Basic Statistics labsD: Basic Statistics notes E: Old Basic Statistics exams Since the professor has forgotten the contents of these flash drives, he is going to check them out one at a time. How many orders are possible? a) b) If the professor has prepared labels for these five flash drives and sticks the labels on in a random fashion, what is the probability that he will end up with all flash drives being correctly labeled? Suppose the prof. is looking for the flash drive containing the old Applied Stat exams. Of the total number of orderings of the five flash drives, in how many instances will drive A be the last one he checks? c) d) What is the probability that drive A will be the last one checked? e) How many distinct orderings of the five flash drives are there if only the particular course is considered (Basic, Applied or Design)? Suppose the profs labels just have the name of the course on them. If he sticks the labels on the flash drives in random fashion, what is the probability that they will be correctly labeled according to course? f) g) Now suppose the prof. has only time enough to check out three of these five flash h) What is the probability that the three that he checks are flash drives C, D& E, in i) Suppose the prof. selects three of the five flash drives at random and sticks those drives. How mony orderings of three of these five are possible? that order? in his briefcase and takes them home. At home he checks them out. How many different groups of three drives are possible? What is the probability that the three flash drives in the prof's briefcase are the three Basic Stat drives? How many of the sets of three that you counted in Part (0) include exactly two Basic Stat drives? k) ) What is the probability that, among the three flash drives he took home, the prof. will find exactly two Basic Stat drives?Explanation / Answer
Solution:-
3)
Total ways of answering Applied stat = 5 × 5 × 5 = 125
Number of correct ways to answer = 1 × 1 × 1 = 1
Probability of getting perfect score in Applied stat = 1/125 = 0.008
Total ways of answering in Abstract quiz = 2 × 2 × 2 × 4 = 32
Number of correct ways to answer = 1 × 1 × 1 = 1
Probability of getting perfect score in Abstract quiz = 1/32 = 0.03125