In an ethnic group, $30$% of the adult male population is known to have heart disease. A test indicates high cholesterol level in $80$% of adult males with heart disease. But the test also indicates high cholesterol levels in $10$% of the adult males with no heart disease. Then the probability, that a randomly selected adult male from this population does not have heart disease given that the test indicates high cholesterol level, equals
$P(\text{Adult male pop with Heard disease)=P(AH)=0.3}$
$P(\text{test indicates high cholesterol level of an adult male with Heard disease)=$P(T|AH)$=0.8}$
$P(\text{test indicates high cholesterol level of an adult male with no Heard disease)=$P(T|AH^{c}$)=0.1}$
To find
$P(AH^c|T)=\dfrac{P(T|AH^c)P(AH^c)}{P(T|AH^c)P(AH^c)+P(T|AH)P(AH)}=\dfrac{0.1\cdot0.7}{0.1\cdot0.7+0.8\cdot0.3}=\dfrac{7}{31}=0.22$
But this answer is wrong I have no idea where is my mistake.Please guide me.