In an airport security system, $2\%$ of passengers carry prohibited items. The detection system correctly identifies $95\%$ of passengers with prohibited items but also has a false positive rate of $3\%.$ If a passenger triggers the alarm, what is the probability that they are carrying prohibited items?

a$.$

$0\mathrm{.}0391$

b$.$

$0\mathrm{.}095$

c$.$

$0\mathrm{.}391$

d$.$

$0\mathrm{.}95$