Question

Marvin lives in Stormwind City and works as an engineer in the city of Ironforge. In the morning, he has 333 transportation options (teleport, ride a dragon, or walk) to work, and in the evening he has the same 333 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 1

The event "Atleast once" is the complement of event "None".

So, the probability that Marvin teleports atleast once per day will the compliment of probability that he does not teleports during the day. Therefore, first we need to find the probability that Marvin does not teleports during the day.

At Morning, the probability that Marvin does not teleport = 2/3

Likewise, the probability tha Marvin does not teleport during evening is also 2/3.

Since the two events are independent i.e. his choice during morning is not affecting his choice during the evening, the probability that he does not teleports during the day will be the product of both individual probabilities.

So, the probability that Marvin does not teleport during the day = $\frac{2}{3}*\frac{2}{3}=\frac{4}{9}$

Probability that Marvin teleports atleast once during the day = 1 - Probability that Marvin does not teleport during the day.

Probability that Marvin teleports atleast once during the day = $1-\frac{4}{9}=\frac{5}{9}$