+42 Person A and Person B have the exact same wardrobe which consists of 2 different pairs of shoes, 3 different pans, and 4 differnt shirts. What is the probability that Person A and Person B wear the same outfit?
I did it by doing: Person A can choose whatever they want to wear, it doesn't matter. The only thing that matters is that after person A chooses their outfit, Person B must choose the same outfit as person A. Therefore, person B has a 1/2*1/3*1/4 = 1/24 chance of choosing the same outfit as person A, and they have a 1/24 chance of wearing the same outfit.
My teacher did it by saying that person A has a 1/24 chance of choosing the same outfit as person B, and then person B had a 1/24 chance of choosing the same outfit as person A, so the answer was therefore 1/576.
Which one of us is right and why? (About half of my class did it the same way I did and our teacher is known for being wrong a lot and being scatterminded, so I just wanted to make sure I know which way is correct so I don't fail the big test at the end of the year.)
