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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!

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  • $\begingroup$ I think you mean "an 80% chance of winning each game" rather than "every game". You also have to assume that the outcome of each game is independent of the others. $\endgroup$ – Gordon Smyth Jul 8 '17 at 22:16
  • $\begingroup$ I assume you are trying to answer the 2017 NBA Hackathon application questions. I wrote up a detailed answer to the applications questions (including this one) in this blog post. In short, @kbiolsi's answer is correct, and you can also run a MC simulation to approximate the answer. $\endgroup$ – Dan Salo Sep 5 '17 at 21:10
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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
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