Let us consider the following experiment: we roll two dice consecutively. The fi

Question

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.

Explanation / Answer

IN FAIR DICE THE PROBABILITY OF EACH NUMBER = 1/6

WHILE AS GIVEN IN THE UNFAIR DICE THE PROBABILITY 0F 1,2,3 = 0 AND PROBABILITY OF 4,5,6 = 1/3 EACH

A)PROBABILITY OF OUTCOME (1,6) = 0

BECAUSE IS 1 COMES UP IN 1ST DICE WE WILL NOT ROLL THE SECONE DICE, WE WILL ROLL THE 1ST DICE AGAIN

B) PROBABILITY OF OUTCOME = (6,1) = 0 AS IF WE GET THE 6 IN 1ST DICE THEN WE WILL ROLL THE 2ND DICE BUT THE PROBABILITY OF GETTING 1 IN SECOND DICE = 0

HENCE TOTAL PROBABILITY = 0

C) PROBABILITY OF OUTCOME (6,6) = 1/6*1/3 = 1/18 AS IN THE 1ST DICE THE PROBABILITY OF GETTING 6 = 1/6 WHILE IN THE SECOND DICE THE PROBABILITY OF GETTING THE 6 = 1/3

HENCE THE ANSWER = 1/18

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