Question

At a railway station a passenger leaves his luggage in a locker which is opened by dialling a three digit code (say 253,009,325 etc.). The passenger chooses the code, tries to open the locker by dialling three digits at random.
let $B=${The locker opens after $k$ trials} be a event. The probability that the lockers opens after k trails is (where k=1000)

Answer 1

$P\left(A\right)=\left(0.1\right)\left(0.1\right)\left(0.1\right)=.001$
If k trails are made, then it is natural to assume that the unsuccessful combinations are not repeated

Now $P\left(B\right)=1-P\left(\overline{B}\right)$
$=1-\frac{999}{1000}.\frac{998}{999}...\frac{1000-k+1}{1000-k+2}.\frac{1000-k}{1000-k+1}$

$=1-\frac{1000-k}{1000}=\frac{k}{1000}$