If I have an array of $n$ numbers in the range [0,1) and have the following events for $y$:
for $i=1$ to $n$ :
generate a new number $y$ in [0,1) uniformly and independent of previous
if $y\ge0.5$ then
toss a fair coin if the coin turns up "HEADS" then
I need to find out what is the probability that y is in the range [0,1/n)
My solution: $1/2+1/2\cdot1/2=3/4$ - the first 1/2 is the probability when y is not greater than 0.5. The second $1/2\cdot1/2$ is the probability when $y>0.5$ AND because of the fair coin - we have 1/2 change of being HEADS.
Is it the correct way ? Do I need to add n into the equation? Please correct me if I am wrong. Thanks!