$\text{Probability of being infected} = 0.5$
$\text{Probability of developing disease} = 0.3$
Only when a person develops disease he will show symptoms of it and whenever a disease is developed we can expect symptoms to be shown.
So, $\text{Probability of not showing symptoms} = 1-0.3 =0.7$
$\text{Probability of being infected and not showing any symptoms} = 0.5 \times 0.7 = 0.35$
Correct Answer: C $35\%$