Utopia Island

The probability of disease A on the island of Utopia is 40%. The probability of occurrence among the men of this island, which make up 60% of all the population (the rest are women), is 50%. What is the probability of occurrence of A disease among women on Utopia Island? Find the result in percent.

Correct answer:

p =  25 %

Step-by-step explanation:

$$\begin{gathered} p_1=40\%=\frac{40}{100}=\frac{2}{5}=0.4 \\ {p}_2=60\%=\frac{60}{100}=\frac{3}{5}=0.6 \\ {p}_3=50\%=\frac{50}{100}=\frac{1}{2}=0.5 \\ n=1000 \\ m=p_2\cdot n=0.6\cdot 1000=600 \\ z=n-m=1000-600=400 \\ {p}_3\cdot m+(p/100)\cdot z=p_1\cdot n \\ 0.5\cdot 600+(p/100)\cdot 400=0.4\cdot 1000 \\ 400p=10000 \\ p=\frac{10000}{400}=25 \\ p=25=25\% \end{gathered}$$

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