Re: Probability Help
I've been drinking a little, so I'm just going to do the eleven game losing streak. I'm also going to assume that this is 11 consecutive losses (not, say loss + tie + ten more losses).
The probability of losing 11/11 at 45.5% is just .455^11, or 0.000173032. Now, to find the probability that you get an 11 loss streak in 150 games, start by considering the case when you start off losing 11 straight games. You'd have to win or tie the 12th, otherwise it would be a 12 game losing streak.
Case 1: lllllllllll(w or t)...
Probability: .455^11*.545*1 = 0.0000943022
Case 2: (w or t)lllllllllllllll(w or t)...
Probability: .545*.455^11*.545*1 = 0.0000513947
Cases 2 through 140 have the same probability, since you flank the 11 game losing streak with ties or wins on either side, and case 1 has the same probability as case 140 which is ...(w or t)lllllllllll
So, our probability of having at least one eleven game losing streak in a game is 2*0.0000943022 + 139*0.0000513947 = 0.00733247, or .73%. Note that the answer to the question "What is the probability of having at least one eleven game or more losing streak?" would be higher.
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