Case study
VIRGIN BLUE KEEPS THE AIR FAIR
1. What probabilities are given in this case? Use these probabilities and the probability laws to determine what percentage of domestic travelers travelled with Virgin blue at least twice in the last 4 years.
○1In this case, there are 3 probabilities have been given.
Within four years of launching the airline, Virgin Blue secured 34% of the market. How many percentage of the market VB got? P(m)=0.34
○②. During this same time period, 30% of domestic air travelers travelled with VB for the first time. P(f)=0.3
○③. During this same time period, 85% of those who initially travelled with VB were flying with VB again. P(s)=0.3*0.85=0.255
What percentage of domestic travelers travelled with Virgin blue at least twice in the last 4 years?
P(t)=1-(1-0.3)-0.3*(1-0.85)=0.255
0.255*100%=25.5%
2. Is age category independent of the willingness to travel with the new airline? Reliable statistics suggest that approximately 12% of all domestic travelers are in the 35-49 age category. Suppose 24% of the domestic traveler who traveled with Virgin blue for the first time during the initial 4-year period were in the 35-49 age category. Use this information to determine whether age is independent of travelling with Virgin blue for the first time during the 4-year period. Explain your answer.
Age category is independent of the willingness to travel with the new airline.
P(A) is 12% of all domestic travelers are in the 35-49 age category.
P(B) is 24% of the domestic traveler who traveled with Virgin blue for the first time during the initial 4-year period were in the 35-49 age category. SO, P(B)=0.3*0.24=0.072
P(A|B)=P(A)∩P(B)/P(B)=0.12*0.072 /0.072=0.12 P(A)=0.12
Since P(A|B)=P(A) The events are independent.
3. Using the probabilities given in (2), calculate the probability that a randomly selected Australian domestic traveler is either in the 35-49 age...