For this question, I know I need to use Geometric Distribution. But I am lost because question asked for the 2nd person i.e 2nd occurrence instead of 1st occurrence. Appreciate anyone's help. Thanks!
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We may search for a very similar exercice : Question 1 : We ask 6 persons, what is the probability to have exactly 1 person in favor of this leisure center ? Question 2 : what is the probability that person n°7 is in favor of this leisure center ? Question 3 : your initial question. – Lourrran Apr 14 '23 at 08:04
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See Binomial Distribution, specifically $\displaystyle \binom{n}{k}p^kq^{(n-k)}.$ You need that exactly $~1~$ of the first $~6~$ people is not in favor, and that the $~7$-th person, specifically, is also not in favor of it. – user2661923 Apr 14 '23 at 08:05
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This is more like the Negative Binomial Distribution. You need $\mathbb P(NB(2,0.2)) = 7$, because you're looking for the second occurrence and the probability of one occurrence is $0.2$. – Sarvesh Ravichandran Iyer Apr 14 '23 at 08:24
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Hint: In order for the 7th person to be the 2nd not in favor, we must have (1) exactly one "not in favor" person among the first 6 people, and (2) the 7th person is not in favor. – awkward Apr 14 '23 at 12:34