Answer:
[tex]\sf (i) \quad \dfrac{1}{7}[/tex]
[tex]\sf (ii) \quad \dfrac{2}{21}[/tex]
[tex]\sf (iii) \quad 315\:people[/tex]
[tex]\sf (iv) \quad 126\: females[/tex]
Step-by-step explanation:
Part (i)
If 6/7 of people who are quarantined do not have the disease then the fraction of people that do have the disease is:
[tex]\begin{aligned} \implies 1-\dfrac{6}{7} & =\dfrac{7}{7}-\dfrac{6}{7}\\\\ & =\dfrac{7-6}{7}\\\\ & =\dfrac{1}{7}\end{aligned}[/tex]
Therefore, 1/7 of people in quarantine have the disease.
Part (ii)
We are told that 2/3 of the people who have the disease come from abroad. Therefore, the fraction of diseased people coming from abroad is 2/3rds of the diseased people:
[tex]\begin{aligned} \implies \dfrac{2}{3} \textsf{ of }\dfrac{1}{7} & = \dfrac{2}{3} \times \dfrac{1}{7}\\\\ & = \dfrac{2 \times 1}{3 \times 7}\\\\ & = \dfrac{2}{21}\end{aligned}[/tex]
Therefore, the fraction of diseased people who have come from abroad is 2/21.
Part (iii)
We are told that 15 people who have the disease do not come from abroad. So if 2/3 of the people who have the disease come from abroad, then 1/3 of the people who have the disease do not come from abroad. Remember that 1/7 of the total people have the disease.
[tex]\begin{aligned} \implies \dfrac{1}{3} \textsf{ of }\dfrac{1}{7} & = \dfrac{1}{3} \times \dfrac{1}{7}\\\\ & = \dfrac{1 \times 1}{3 \times 7}\\\\ & = \dfrac{1}{21}\end{aligned}[/tex]
Therefore, 1/21 of the total number of people have the disease and do not come from abroad.
Therefore, 15 people are equal to 1/21 of the total number of people:
[tex]\implies \sf Total\:number\:of\:people=15 \times 21 = 315[/tex]
Therefore, the total number of people in quarantine is 315.
Part (iv)
If 3/5 of the total are male, then 2/5 must be female.
[tex]\begin{aligned} \implies \dfrac{2}{5} \textsf{ of }315 & = \dfrac{2}{5} \times 315\\\\ & = \dfrac{2 \times 315}{5}\\\\ & = \dfrac{630}{5}\\\\& = 126 \end{aligned}[/tex]
Therefore, 126 females are in quarantine.
