Consider the experiment where a pair of fair dice is thrown. Let X denote the random variable whose value is determined by taking the maximum of the spots showing on either of the two dice thrown. For example, if a 3 and a 5 were thrown, then X would take the value of Maximum(3,5) = 5. The range of values that X can assume are the positive integers {1,2,3,4,5,6}.
1. 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) =
2. Further, find the probability that X is divisible by 4. Probability that X is divisible by 4 =