Question: ENM 5030 - Probability and Statistics (Homework #4) Fall Semester, 2023 M. Carchidi - Problem #1 (20 points) - Balls And Urns Four balls are

ENM 5030 - Probability and Statistics (Homework #4) Fall Semester, 2023 M. Carchidi - Problem #1 (20 points) - Balls And Urns Four balls are randomly chosen, without replacement from an urn that contains 4 red, 5 white and 6 blue balls. Compute the probability that at least one ball of each color is chosen. - Problem #2 (20 points) - Predicting The Weather As a simplified model for weather forecasting, suppose that the weather (either wet or dry) tomorrow will be the same as the weather today with probability p. Suppose that the weather is dry on January 1st and let P n be the probability that the weather is dry n days later. a.) (10 points) Show that P n satisfies the recurrence relation P n 2p 1P n1 1 p for n 2, 3, 4, . . . . b.) (10 points) Sol

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