Given Pr (A) = 0.30, Pr(B - A) = 0.50, and Pr(An B) = 0.15. Find the specified probabilities. a. Pr(A U B) A b. Pr(A - B) B c. Pr (A' U B') d. Pr (A' UB)Given events A and B, with Pr(A) = 0.20 and Pr(B) = 0.60. a. If A and B are independent, find Pr(An B) and Pr (A U B) b. If A and B are disjoint, find Pr(An B) and Pr (A U B)If events A, B, and C form a partition of a universal set U, with Pr(A) = 0.35 and Pr(B) = 0.45. Find the specified probabilities. a. Pr(AnBnC) A b. Pr (A UB UC) B c. Pr (A UB) d. Pr (C)Two dice are rolled, and the sum of the faces is observed. a. What are the odds against rolling a 7? b. What are the odds in favor of rolling a 4 or higher? 0. If the sum of the faces is 7. Find the probability that one of the faces is a two. Given Pr(A) = 0.40, Pr(B) = 0.50, and Pr(A' U B') = 0.70. Find the specied probabilities. a. Pr(B I A) \fThe table below gives the results of a six-point finite quiz. Construct a histogram showing the frequency for each score. Find the mean score. Score Frequency Score X Frequency 0 12 20 2 38 3 40 4 45 5 55 6 40 Total =250A random variable X has the probability density function shown below. Find the expected value and standard deviation of the random variable X Pr (X ) X . Pr(X) X - ul ( X - M)2 (X - M)2 . Pr(X) -2 0.3 3 0.4 4 0.2 6 0.1Two coins are selected randomly from a pocket containing one dime and four quarters. The random variable X is the total value in cents of the 2 selected coins. Find E (X). Outcome X Pr (X) X - Pr(X)