Probability on a number line.
A marker is placed at the origin of a number line. A fair six-sided die is rolled seven times. On each toss, if a 1 or 2 is tossed, the marker is moved one unit to the right, otherwise, the marker is moved one unit to the left.
a) Determine the possible positions on the number line where the marker could end up after the seven tosses.
b)What is the probability that the marker will end up 5 or 6 units to the left of the origin?
c) What is the probability that the marker will end up 3 or fewer units from the origin?
d) Determine the expected value of this random experiment.