Consider the experiment where a fair coin is tossed.
If the toss results in a head, then 1 die is thrown.
If the toss results in a tail, then 2 dice are thrown.
Let X denote the random variable that
counts the number of spots showing on the thrown die or dice.
The range of values that X can assume are the
positive integers from 1 to 12 inclusive.
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 = 7) =
Pr(X = 8) =
Pr(X = 9) =
Pr(X = 10) =
Pr(X = 11) =
Pr(X = 12) =

Further, find the probability that X is divisible by 3.
Probability that X is divisible by 3 equals