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public:calculating_the_size_of_a_set_by_observing_the_proportionality_change_of_its_disjoint_subsets [2019/04/17 02:00] fangfufu [Solution] |
public:calculating_the_size_of_a_set_by_observing_the_proportionality_change_of_its_disjoint_subsets [2019/04/17 02:08] (current) fangfufu [Formal Problem statement] |
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We can consider everyone who voted in an Instagram poll as a set, and the two options are disjoint subsets of the superset. | We can consider everyone who voted in an Instagram poll as a set, and the two options are disjoint subsets of the superset. | ||

- | ===== Formal Problem statement ===== | + | ===== Formal problem statement ===== |

Set $A$ consists of disjoint subsets $a_1, a_2, ..., a_n$. Although we do not know the cardinality of set $A$ (denoted by $|A|$) and the cardinality of each of the subset, we do know the proportion of each subset in terms of set $A$, that is we know $\frac{|a_1|}{|A|}, \frac{|a_2|}{|A|}, ... \frac{|a_n|}{|A|}$. We are allowed to add $n$ elements into subset $a_1$, and observe its change in proportionality. What is the cardinality of set $A$ before elements were added to $a_1$? | Set $A$ consists of disjoint subsets $a_1, a_2, ..., a_n$. Although we do not know the cardinality of set $A$ (denoted by $|A|$) and the cardinality of each of the subset, we do know the proportion of each subset in terms of set $A$, that is we know $\frac{|a_1|}{|A|}, \frac{|a_2|}{|A|}, ... \frac{|a_n|}{|A|}$. We are allowed to add $n$ elements into subset $a_1$, and observe its change in proportionality. What is the cardinality of set $A$ before elements were added to $a_1$? | ||