Marvin lives in Stormwind City and works as an engineer in the city of Ironforge. In the morning, he has 3 transportation options (teleport, ride a dragon, or walk) to work, and in the evening he has the same 3 choices for his trip home. If Marvin randomly chooses his method of travel in the morning and in the evening, what is the probability that he teleports at least once per day?

Answer:The probability is [tex]P=\frac{5}{9}[/tex]Step-by-step explanation:Marvin has to randomly choose between 3 transport options. Since the choice is random, then the probability of choosing any of the three options is the same. The probability of teleportation in the first attempt is: [tex]P_t = \frac{1}{3}[/tex]So, the probability that you do not teleport is [tex]q = 1-p\\\\q = 1-\frac{1}{3}\\\\q = \frac{2}{3}[/tex]The probability that Marvin does not teleport when going to work and Marvin does not teleport when he returns from work is:[tex]P = \frac{2}{3} * \frac{2}{3}\\\\P = \frac{4}{9}.[/tex]Therefore the probability of teleportation at least once is: [tex]P= 1-\frac{4}{9}\\\\P = \frac{5}{9}[/tex]