Statistics Demystified, 2nd edition Stan Gibilisco Explanations for Quiz Answers in Chapter 3 1. If we compare two results (called outcomes) in an experiment and the probability of one outcome has no effect on the probability of the other outcome, then we define the two outcomes as independent. The correct choice is B. 2. By definition, a single element of a sample space constitutes an outcome. In a single experiment, or in the course of multiple identical experiments, the sample space is the set of all possible outcomes. The correct choice is B. 3. If we know the number C of possible combinations that exist in a situation where we take t objects u at a time, we can multiply C by u! (u factorial) to determine the number P of permutations in the same situation: P = (u!) C The correct choice is D. For any positive integer u, u! = 1 x 2 x 3 x 4 x ... x u If u = 0, then we define u! = 1. If a given quantity does not equal a positive integer or 0, then that quantity has no defined factorial. 4. In Fig. 3-13 on page 104, the shaded rectangle has 1/10 the area of the large rectangle (whose two bottom vertices bear the labels xmin and xmax). Therefore, the probability of any particular outcome falling between x = a and x = b is 1/10, or 10%. We should call this probability figure"approximate" because the drawing doesn't indicate precise numerical values. The correct choice is B. 5. In a uniform distribution, the function holds constant for all values of the random variable between a specified minimum and a specified maximum. In Fig. 3-13, this fact shows up in the form of a "flat top" (horizontal line) from the minimum value point xmin to the maximum value point xmax. The probability that an outcome will fall between x = a and x = b equals the ratio of the area of the shaded region to the area of the large rectangle. That's the same as the ratio of the quantity b - a to the quantity xmax - xmin. The correct choice is C. 6. A mathematical probability figure, expressed as a ratio or proportion, always lies between 0 and 1 inclusive. For a particular outcome x, we can have absolute confidence that 0 ≤ pmath(x) ≤ 1 where pmath(x) represents the mathematical probability of x. The correct choice is B. 7. Statisticians determine mathematical probability figures on the basis of pure theory (that is, entirely on the results of hypotheses, logic, and calculations). The correct choice is A. 8. Let's use the formula that tells us how to calculate the number of permutations qPr for a set of q items taken r at a time. That formula, which appears on page 92, is qPr = q! / (q - r)! In this case, we have six objects taken five at a time, so q = 6 and r = 5. When we input those values to the above formula, we get qPr = 6! / (6 - 5)!= 6! / 1!= 6!= 1 x 2 x 3 x 4 x 5 x 6= 720 The answer is C. 9. To determine the number of combinations qCr for a set of q items taken r at a time, we divide the number of permutations qPr by r!. The formula, which we can find on page 92, is qCr = qPr / r! When we derived the answer to Question 8, we calculated 6P5 = 720. Therefore 6C5 = 6P5 / 5!= 720 / 5!= 720 / (1 x 2 x 3 x 4 x 5)= 720 / 120= 6 The answer is A. 10. As defined on page 71, an event is a single test or trial in an experiment, or in the course of multiple identical experiments. The correct choice is A.