Stanton D. answered • 02/11/21
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Hi Dhaval R.,
So translate the expected wins into math expressions. For the first 39 games, # expected wins = 39*0.65, right? BUT, if he wins the last game (P=0.65), then he has the sum of a geometric series for his expected further wins. You can handle that, right?
-- Cheers, --Mr. d.
Stanton D.
Whoa, we both misinterpreted the problem! When it said, he _plans_ to play 39 games, you should think: he will definitely play those, so that's = 39 right there (my initial answer was wrong, I thought number of wins was requested, but it's expected number of games played!). But THEN he has the geometric series as a further possibility, so that's 0.65 + 0.65^2 + .... and that is r + r^2 +r^3 ... = 1/(1-r) = 2.857... so the sum is 41.857... rounds to 41.86. Person who supplied "41.85" as correct answer doesn't know how to round, maybe? -- Cheers, --Mr. d. P.S. Unrealistic scenario! if he comes out of a 39-game round-robin into a playoffs, one might expect his odds of winning to decrease....
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02/14/21
Dhaval R.
Well, I tried this way , take x as R.V for number of games won , then P(X=1) =0.65=p and P(X=2)=p×p , P(X=3)=p^3 ... P(X=39)=p^39. So expected value of X = p+2p^2+3p^3+...+39p^39 = p(1-p^39)/(1-p)^2 which turns out to be 5.306 and adding 1 to get the matches played so 6.305 but this isn't the correct answer , correct answer is 41.85 and I dont know how to do that.02/11/21