QUESTION 10 Consider two events X and Y that have marginal probabilities of 0.68 and 0.57 respectively. Their joint probability is 0.35. Calculate the probability that event X occurs if Y has occurred. (3 decimal places)QUESTION 11 The number showing on the upper face of a fair sixsided dice is observed when rolled. Consider events A and B defined as: o A = the number observed is at most 2 o B = the number observed is an even number Find '|.P(A') [3 decimal places) 2. P(A or B] (3 decimal places) QUESTION 1 The distribution of the distance travelled by 35 people from an outer Brisbane suburb was found to be symmetrical. Five people who were previously travelling the longest distance moved further away and travelled even further. If the distribution of distance travelled is recalculated using the new set of observations for the same sample of people, the shape of the new distribution: 0.3. would remain symmetrical O b' would be right skewed O C' would be left skewed O Cl'is not able to be determined QUESTION 9 Previous studies have found 26% ofall people prefer Coke to all other cola drinks. A random sample of 20 people is selected. What is the probability exactly three people in this sample prefer Coke? (3 decimal places] QUESTION 4 Consider the following statements concerning the binomial distribution: A. The binomial distribution will be symmetrical if only np > 5. B. To ensure the independence of each outcome for a binomial distribution, the observations are randomly selected either from an infinite population without replacement or from a finite population with replacement. C. The sample size for the binomial distribution consists of a fixed number of identical trials. only C is true O only A and B are true only A and C are true only B and C are true O all of the statements are trueQUESTION 1' The probability that tomorrow will be a rainy day is 0.51. The probability tomorrow will be a windy day is 0.22. The probability that it will rain and be windy tomorrow is 0.1 5. What is the probability it will be windy or rainy or both tomorrow? [2 decimal places) QUESTION 8 To ascertain the effectiveness of a new, quicker, and simpler test for identifying diabetes, a study was undertaken involving 904 participants. With this test, a positive result indicates the presence of diabetes. A negative result indicates the absence of diabetes. Data collected to assess the effectiveness of this new test revealed: - 335 of the participants conrmed they actually had diabetes, with the other participants conrming they actually did not have diabetes. - 12 participants actually had diabetes and produced a negative test result. - 451 participants produced a negative test result. A participant from the study is chosen at random. What is the probability the participant actually has diabetes or the test is positive? (3 decimal places) QUESTION 2 Given the typical form of the distribution of income (right skewed), the median : O a. will be less than the mode O b. will be greater than mean O C. is not the most appropriate measure of central tendency O d. None of the above