Question

A small airport is served by four airlines: A, B, C which offer overseas flights, and D which offers domestic flights.

Over a one month period, the number of on-time and delayed arrivals are recorded for all four airlines. They are shown in the table below.

What is the probability that a flight was delayed and it was run by airline D? Give your answer correct to four decimal places.

Airline On-Time Delayed

A 105 15

B 38 20

C 21 7

D 200 59

Answer 1

$\text{let }S -\text{number of all aircraft departures}$

$S = 105+15+38+20+21+7+200+59=465$

$\text{let }S_d -\text{number of all delayed aircraft departures}$

$S_d=15+20+7+59=101$

$\text{delayed departure probability:}$

$P_d=\frac{S_d}{S}=\frac{101}{465}$

$\text{probability of delayed company D flight}$

$P_d(D)=\frac{S_d(D)}{S_d}=\frac{59}{101}$

$\text{the probability that the flight is delayed }\newline \text{and serviced by company D:}$

$P_d*P_d(D)=\frac{101}{465}*\frac{59}{101}\approx0,1269$

Answer:$\approx0,1269$