Question

The airline industry defines an on-time flight as one that arrives within 15 minutes
of its scheduled time. The following table shows the number of on-time and late
flights leaving New York and arriving in Miami between November 1 and
December 31, 2018, by airlines:
	Airlines		On-Time	Late	Total
	United		254	72	326
	Delta		292	65	357
	American		235	58	683
	Total		781	195
a.      What is the probability that a randomly selected flight was Delta and was late?
b.      What is the probability that a randomly selected flight was United or was on-time?
c.      Given the flight was late, what is the probability that it was from American?
d.      Given the flight was from Delta, what is the probability that it was late?
e.      Construct a probability tree for these probabilities.

Answer 1

Total flights = 781 + 195 = 976

A)

P( flight was delta and was late ) = 65 / 976

B)

P( United airlines ) = 326 / 976

P( flight was on time ) = 781 / 976

P( United airline and flight on time ) = 254 / 976

So,

P( flight was united or was on time )

= P( united airlines ) + P( flight was on time ) - P( United airline and flight on time )

= 326 / 976 + 781 / 976 - 254 / 976

= 853 / 976

C)

P(American flight ) = 293 / 976

P( flight was late ) = 195 / 976

P( American flight and flight was late ) = 58 / 976

So, P( American flight l flight was late )

= P( American flight and flight was late) / P( flight was late )

= (58 / 976) / (195 / 976)

= 58 / 195

D)

P( flight was delta and late ) = 65 / 976

P( flight was delta ) = 357 / 976

So, P( flight was late l flight was delta )

= P( flight was delta and late ) / P( flight was delta)

= (65 /976 ) / ( 357 / 976 )

= 65 / 357