On a TV game show, the contestant is asked

to pick one of three doors. Behind each door
are two large boxes to choose from. The
grand prize is in one of the boxes behind
Door 1. There are good prizes in one box
behind Door 2 and one box behind Door 3.
The other boxes all contain gag prizes.

2 answers

What is the probability of winning the
grand prize?
d) What is the probability of winning a
good prize?
e) What is the probability of winning a gag
prize?
f) What is the sum of all the probabilities?
well, one box out of six = 1/ 6
or
right door = 1/3 then right box = 1/2 and indeed 1/3*1/2 = 1/6 anyway.

two out of six = 1/3
or
2/3 for one of the other doors then 1/2 for the right box = 1/3

If there is to be some outcome, any old outcome, the sum is one :)