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45% of the students failed in statistics, 35% in computer and 25% in both statistics and computer courses. A randomly selected student, a) If it fails from the computer, the probability of failing the statistics, b) If it fails from statistics, the probability of failing from the computer, c) Find the probability of failing at least one of these two courses.

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ED The probability that an IT student likes statistics is 0.45, the probability that he likes Calculus is 0.35 and that he likes either Statistics or Calculus is 0.50. A student from IT College is selected at random, a) find the probability that he likes both Statistics and Calculus bj Determine whether the events "like statistics" and "like Calculus" are independent. Explain. c) Find the probability that the selected student like Statistics but not Calculus d) Find the probability that the selected student likes neither Statistics nor Calculus e) it is found that the selected student likes Statistics, what is the probability that he likes Calculus.3 (20 p) 45% of the students failed in statistics, 35% in computer and 25% in both statistics and computer courses. A randomly selected student, a) If it fails from the computer, the probability of failing the statistics, b) If it fails from statistics, the probability of failing from the computer, c) Find the probability of failing at least one of these two courses.(A) 0.02 (B) 0.4 (C) 0.5 (D) 0.6 (E) 0.98 35. Suppose the probability that you will receive an A in AP Statistics is 0.35, the probability that you will receive A's in both AP Statistics and AP Biology is 0.19, and the probability that you will receive an A in AP Statistics but not in AP Biology is 0.17. Which of the following is a proper conclusion? (A) The probability that you will receive an A in AP Biology is 0.36. (B) The probability that you didn't take AP Biology is .01. (C) The probability that you will receive an A in AP Biology but not in AP Statistics is 0.18. (D) The given probabilities are impossible. (E) None of the above PROBABILITY AS RELATIVE FREQUENCYThe probability of a student passing statistics is known to be 0.47; and the probability of a student passing chemistry is known to be 0.43. If the probability of passing both is known to be 0.32, calculate: (a) the probability of failing chemistry (b) the probability of passing at least one of statistics and chemistry (c) the probability of a student passing chemistry, given that they passed statistics (d) Are passing chemistry and statistics independent? Justify (e) (harder) a group of 32 randomly selected students attend a special seminar on study skills. Of these 32, only 8 fail both. State a sensible null hypothesis, test it, and interpret