# Thread: Probability on a number line.

1. ## 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.

2. Originally Posted by digitalis77
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.

Let X be the random variable position of marker after seven rolls.

Let Y be the random variable number 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) = ......

3. Originally Posted by digitalis77
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.

Determine the expected value of this experiment.
The expected value after one roll is $(P(1) + P(2))\cdot 1 + (P(3) + P(4) + P(5) + P(6))\cdot -1$, which is

$\frac{1}{3} - \frac{2}{3} = -\frac{1}{3}$. So the expected value of the experiment after 7 rolls is $-\frac{7}{3}$.