Q$-4)$ A particular city is serviced by three airlines for its passenger traffic. Airline A carries $50\%$ of the passengers, Airline B $30\%$ and Airline C remaining $20\%.$ Each of the airline is responsible for handling its security. The probabilities that a passenger carrying some type of weapon will be detected by Airline A$.$B and $C$ are $0\mathrm{.}9,0\mathrm{.}5,0\mathrm{.}4$ respectively. $(15$pts$)$