I'm trying to determine the probability that the prediction is true, that Warriors won't lose consecutive games during an 82 game season. Assuming that Warriors have an 80% chance of winning every game I was trying to get an approximation using binomial probability (nCr*p^x(1-p)^n-x) but I don't know how to model consecutive lose trials and I'm not sure if this is the best approach. Any help would be appreciated, thanks!
A couple of different formulas (one recursive, one not) that will allow you to compute the "chance of getting a run of K or more successes in a row in N Bernoulli trials" can be found at the following link: http://www.askamathematician.com/2010/07/q-whats-the-chance-of-getting-a-run-of-k-successes-in-n-bernoulli-trials-why-use-approximations-when-the-exact-answer-is-known/
The probability that the Warriors will not lose two or more games in a row during an 82-game season given a probability of 0.8 of winning any given game and assuming games are independent of one another is 0.05882.
Here are the probabilities for different numbers of games played:
no. games probability 2 0.96000 3 0.92800 4 0.89600 5 0.86528 10 0.72666 20 0.51250 30 0.36145 40 0.25492 41 0.24617 50 0.17979 60 0.12680 70 0.08943 80 0.06307 82 0.05882