In a population $,$ two diseases D$1$ and D$2$ are present in $40\%$ and $20\%$ respec$-$

tively. It is assumed that the number of those who suffer from both diseases

is negligible $($i$.$e; D$1\backslash$cap D$2=).$ We undertake a screening system of D$1$ and

D$2$ diseases. To do this, we apply a test that works on $80\%$ of D$1$ patients, on

$95\%$ of D$2$ patients, and in $11\%$ of individuals who have neither of these two

conditions.