Suppose you roll a fair 6-sided die and accumulate the sum until you've reached a sum $>= 1000$. What is the probability your final roll is a $6$?
your final roll must be on an integer in $[994, 999]$. From $999$ all rolls sum to at least $1000$ so there are $6$ outcomes, $994$ has just one outcome. Total number of outcomes is $6+5+4+3+2+1$ $6$ of which involve rolling a $6$ thus probability is $\frac6{21}$ Is this a valid solution?