There are given following informations: The probability that ill person is recognised as ill is $0.64$. The probability that healthy person is recognised as healthy is $0.89$. The probability of a disease is $P (K) = \frac{3}{40}.$ Calculate the probability that a randomly selected test is positive and comes from healthy person.
My idea and question:
$A$-ill,$B$-positive Test.
$P(A)=\frac{3}{40}\Rightarrow P(A^{c})=\frac{37}{40}$
$P(A| B)=0.64\Rightarrow P(A^{c}| B)=0.36$
$P(A^{c}| B^{c})=0.89\Rightarrow P(A| B^c)=0.11$
$P(B|A^{c})=?$
$P(P|A^{c})=\frac{P(A^{c}|B)P(B)}{P(B|A)P(A)+P(B|A^{c}P(A^{c}))}$
But how do I find $P(B|A)$ and $P(B|A^{c})$?