Consider the experiment where a pair of dice is thrown. Let X denote the random

Question

Consider the experiment where a pair of dice is thrown. Let X denote the random variable whose value is determined by multiplying the number of spots showing on the one die by the number of spots showing on the other. The range of values that X can assume are the positive integers 1, 2, 3,4,5,6,8,9,10,12,15,16,18,20,24,25,30,36. Please give the corresponding probabilities for the values of X given below. Pr(X = 1) = Pr(X = 2) = Pr(X = 3) = Pr(X = 4) = Pr(X = 5) = Pr(X = 6) = Pr(X = 8) = Pr(X = 9) = Pr(X = 10) = Pr(X = 12) = Pr(X = 15) = Pr(X = 16) = Pr(X = 18) = Pr(X = 20) = Pr(X = 24) = Pr(X = 25) = Pr(X = 30) = Pr(X = 36) = Further, find the probability that X is divisible by 2. Probability that X is divisible by 2 equals Answers) submitted:

Explanation / Answer

Consider all 36 results:

Hence, the table:

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Of these 36, 27 have even products. Hence,

P(x is even) = 27/36 = 3/4 [ANSWER]

Die 1 Die 2 X 1 1 1 1 2 2 1 3 3 1 4 4 1 5 5 1 6 6 2 1 2 2 2 4 2 3 6 2 4 8 2 5 10 2 6 12 3 1 3 3 2 6 3 3 9 3 4 12 3 5 15 3 6 18 4 1 4 4 2 8 4 3 12 4 4 16 4 5 20 4 6 24 5 1 5 5 2 10 5 3 15 5 4 20 5 5 25 5 6 30 6 1 6 6 2 12 6 3 18 6 4 24 6 5 30 6 6 36

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