As of this post, the Golden State Warriors have 68 wins and need to win at least 5 of their remaining 7 games to break the record for most wins in a season. This article estimates the Warriors' chance of winning each of those 7 games and ultimately gives them an 85% chance of breaking the record.
That got me thinking of how to efficiently solve the general version of this problem. That is, suppose a team has $n$ games with a probability $P_i$ of winning the $i$th game, $1 \leq i \leq n$, with the outcome of the games independent of each other. What is the probability of the team winning between $m_1$ and $m_2$ games where $0\leq m_1\leq m_2 \leq n$?
The naive approach would be to sum the probabilities of each valid combination of games, but that would be computationally inefficient. Another approach would be to run a Monte Carlo simulation, but that does not give you an exact result. I'm looking for an efficient algorithm/formula that would give you the exact answer to this problem; however, I am inclined to believe that this problem is NP Complete.