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Omni-MATH / Lil Wayne, the rain god, determines the weather. If Lil Wayne makes it rain on…

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problem

Lil Wayne, the rain god, determines the weather. If Lil Wayne makes it rain on any given day, the probability that he makes it rain the next day is 75%75 \%. If Lil Wayne doesn't make it rain on one day, the probability that he makes it rain the next day is 25%25 \%. He decides not to make it rain today. Find the smallest positive integer nn such that the probability that Lil Wayne makes it rain nn days from today is greater than 49.9%49.9 \%.
Plain-text mathematical notation (without MathML)
Lil Wayne, the rain god, determines the weather. If Lil Wayne makes it rain on any given day, the probability that he makes it rain the next day is 75%. If Lil Wayne doesn't make it rain on one day, the probability that he makes it rain the next day is 25%. He decides not to make it rain today. Find the smallest positive integer n such that the probability that Lil Wayne makes it rain n days from today is greater than 49.9%.
Original LaTeX notation
Lil Wayne, the rain god, determines the weather. If Lil Wayne makes it rain on any given day, the probability that he makes it rain the next day is $75 \%$. If Lil Wayne doesn't make it rain on one day, the probability that he makes it rain the next day is $25 \%$. He decides not to make it rain today. Find the smallest positive integer $n$ such that the probability that Lil Wayne makes it rain $n$ days from today is greater than $49.9 \%$.

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