Probability of infected but does not show symptoms of disease? A person moving through a tuberculosis prone zone has a $50\%$ probability of becoming infected. However, only $30\%$ of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease? 1. $15$ 2. $33$ 3. $35$ 4. $37$ * * * My attempt : Given, only $30\%$ of infected people develop the disease, so probability of infected people is $= 0.3\times0.5 = 0.15$. Therefore, required probability is $=1-0.5-0.15=0.35$ > Can you explain in formal way, please?

The way you worded that is a little strange.

I have an alternative approach.

Let $I$ be the event that a person is infected, $D$ be the event that a person develops the disease, and $\bar I, \bar D$, not those events. Then $$P(I\bar D)= P(\bar D|I)P(I) = (1-P(D|I))P(I) = (1-.30)(.5) = 0.35 = 35\%$$ where in the second step I used the product rule.