Answer to Question #233971 in Statistics and Probability for Milika

Question

A consume ragency randomly selected 1700 flights for two major airlines, A
Minutes Late 1Hour Late 1Hour Late
Airline B 39 33 16 80
andB.
The following table gives the two-way classification of these flights
Includes flights that arrived early or on time.
Less Than 30, 30 Minutes to More Than
that this flight is
based on airline and arrival time. Note that” less than 30 minutes late”in
Airline A 42 93 90 92
If one flight is selected at random from these 1700 flights, find the probability
(i) not more than 1hour late
(iv) more than 1hour late given that it is a flight on airline A
(ii) is not less than 30 minutes late
(iii) a flight on airline B given that it is 30 minutes to 1hour late
[2marks]
[2marks]

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)

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

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

(iv)

$$P(\text{more than 1hour late}|A)=\dfrac{92}{911}$$