1. (15pm) The duration of videos in a dataset is measured in minutes {and fractions of minutes}. Let the sample space be positive, real numbers. Dene the events A and B as follows: A = {r|r s: 15.5} and B = {.r|r E 5.1'5}. Describe each of the following events in your words: {a} A {b} B\" [c] A U B [d] A r1 B. 2. (lpts) Of the students in an Ecology class, 60% took statistics, 45% took calculus and 25% took both. Select a student randomly. Consider the following 2 events: In G: selected student took at least one of the courses I H: selected student took none of the courses Find 13(3) and P[H]. 3. (lpts) Two dice are rolled. Consider the following 3 events: I' A = 'sum of the two dice equals to 3' I B = 'sum of the two dice equals to 3' o C = 'at least one of the dice shows 2'. Answer the following questions: [a] 'What are the sample space and the events A, B, and C? {b} \"mat is FIAIC}? [c] \"mat is F{B|C']I? [d] Are A and C independent? 1What about B and [3? Explain your answer. 4. (lpts) A patient is seen at a clinic. A recent epidemic in town shows that the probability that the patient suffers from the flu is 535. The probabilityr that he suffers from walking pneumonia is I3.55. The probability that he suffers from both is 0.50. Denote by F the event that the patient suffers from the u and by Mr that he suffers from pneumonia. [a] Compute P{F|M). [b] Compute PfMIF]. [c] Are F and M independent? Explain. 5. {lpts} Samples of laboratory glass are in small, light packaging or heavy, large packaging. Suppose that 2% and 1% of the sample shipped in small and large packages, respectively, break during transit. If 50% of the samples are shipped in large packages and 45% are shipped in small packages, what proportion of samples break during shipment