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[2K12) Two different airlines have a flight from San Francisco to New York that departs each weekday morning at a certain time. There is a 70% chance that the hrst airlines flight is fully booked on a particular day, and there is a 60% chance that the second airlines flight is fully booked on that same day. Moreover, when the first airlines flight is full, there is a 77% chance that the second one is also full. a) What is the probability that a seat is available for you on one weekday if you have to ly from San Francisc o to New York using one of these airlines? b) What is the probability that the first airlines flight is fully booked if you find out that the second one is fully booked?

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(a) The Probability of first airlines flig htP (A70/100 0.7 The Probability of second airlines flight- P (B)-6 0/1000.6 Probability o f th ata seat available P (A)P (B) P (A B) 0.7 0.6 (0.7*0.6) 1.3 0.42 -0.88 (b) Probability of first airlines flight fully booked = 100/100-1 Probability of second airlines flight fully booked = 77/100-0.77

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