Question

A consumer agency randomly selected 1700 flights for two major airlines, A
and B. The following table gives the two-way classification of these flights
based on airline and arrival time. Note that ”less than 30 minutes late” in-
cludes flights that arrived early or on time.
Less Than 30 30 Minutes to More Than
Minutes Late 1 Hour Late 1 Hour Late
Airline A 429 390 92
Airline B 393 316 80
If one flight is selected at random from these 1700 flights, find the probability
that this flight is
(i) not more than 1 hour late

(ii) is not less than 30 minutes late

(iii) a flight on airline B given that it is 30 minutes to 1 hour late

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c: c} & Less \ than & 30\ minutes & More \ than & Total \\ & 30 \ minutes& to\ 1\ hour & 1\ hour \\ & late & late & 1\ hour \\ \hline Airlane\ A & 429 & 390 & 92 & 911 \\ \hdashline Airlane\ B & 393 & 316 & 80 & 789 \\ \hdashline Total & 822 & 706 & 172 & 1700 \\ \end{array}$$

(i)

$$P(\text{not more than 1hour late})=\dfrac{822+706}{1700}$$

$$=\dfrac{382}{425}$$

(ii)

$$P(\text{is not less than 30 minutes late})=1-\dfrac{822}{1700}$$

$$=\dfrac{439}{850}$$

(iii)

$$P(\text{ B | 30 minutes to 1hour late})=\dfrac{316}{706}$$

$$=\dfrac{158}{353}$$