Question

a) 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” includes 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 [1 mark] (ii) is not less than 30 minutes late [1 mark] (iii) a flight on airline B given that it is 30 minutes to 1 hour late [2 marks] (iv) more than 1 hour late given that it is a flight on airline A 

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)

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

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

(ii)

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

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

(iii)

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

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

(iv)

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