Probability of picking a certain option at least once in two tries

Question

I'm doing probability problem on Khan Academy and a little bit confused. The problem is following:

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?

My answer was $1/9$ because morning probabilty of random choice of teleportation is $1/3$ and evening's $1/3$ either multiplying them leads to $1/9$ however the correct answer is $5/9$

this is a diagram

Your calculation gives the probability that he teleported to work and teleported back. That's what multiplying the probability of two events does. — alexis, Nov 20 '15 at 10:47
Possible duplicate of Probability of of an event happening at least once in a sequence of independent events? — , Nov 20 '15 at 12:23
You have listed the nine possible options. How many of them involve teleporting at least once? — user247327, Nov 20 '15 at 12:43

score 1 · Answer 1 · edited Mar 20 '19 at 06:21

1

It says "at least once," which means it could be in the morning or evening or both. There are $5$ choices that have at least one teleport in the day - rows $1$, $2$, $3$, $4$, and $7$ in the list given - and there are nine total outcomes, so the answer is $5/9$.

edited Mar 20 '19 at 06:21

PrincessEev

43,815

answered Mar 20 '19 at 05:37

Kat the kit

11
1

Probability of picking a certain option at least once in two tries

1 Answers1