Let us consider the following experiment: we roll two dice consecutively. The first die is fair. If the first roll is a 1, 2, or 3, we roll the same die again. If the first roll yields a 4, 5, or 6, then we roll an unfair die with probabilities [0 0 0 1/3 1/3 1/3]. What is the probability of the outcome (1,6) (the first roll is a 1 and the second is a 6)? What is the probability of the outcome (6,1)? What is the probability of the outcome (6, 6)? In addition to calculating these probabilities analyticaly, please write a matlab script to simulate this experiment. Run 1000 trials of this experiment and estimate the same probabilities you calculated analytically.
Let us consider the following experiment: we roll two dice consecutively. The first die is fair. If the
first roll is a 1, 2, or 3, we roll the same die again. If the first roll yields a 4, 5, or 6, then we roll an unfair die with probabilities [0 0 0 1/3 1/3 1/3]. What is the probability of the outcome (1,6) (the first roll is a 1 and the second is a 6)? What is the probability of the outcome (6,1)? What is the probability of the outcome (6, 6)? In addition to calculating these probabilities analyticaly, please write a matlab script to simulate this experiment. Run 1000 trials of this experiment and estimate the same probabilities you calculated analytically.
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