Let X be the random variableposition of marker after seven rolls.

Let Y be the random variablenumber of times the marker moves right. Note that Y ~ Binomial(n = 7, p = 1/3).

Thinking about the possible values of Y should show you that the possible values of X are -7, -5, -3, -1, 1, 3, 5, 7. It should also let you calculate the probability of each value of X. Then it should be straight forward to calculate:

b) Pr(X = -5) = ......

c) Pr(X = 3 or 1 or -1 or -3) = ......

d) E(X) = ......