To attend a business meeting in Los Angeles, a business traveler based in
Cincinnati must first fly to Chicago and board a connecting flight. Because
of the nature of the flights, the traveler has very little time to change
planes in Chicago. On his way to the airport, he ponders the possibilities.
On the basis of past traveling experience, he knows that there is a 70%
chance that his plane will be on time in Chicago P(on time in
Chicago)=0.70. This leaves a 30% chance that his Cincinnati-based plane
will arrive late in Chicago. Knowing that if he arrives late, he may not be
able to make the connecting flight to Los Angeles, he decides that the
probability that he will be late in Chicago and on time in Los Angeles is
20% P(Chicago late and LA on time)=0.20. Suppose that the traveler
arrives late in Chicago. Given that he arrived late in Chicago, what is the
probability that he will reach LA on time?
Conditional probability of two events:
The conditional probability is the probability of one event given that the other event has already occurred.
Consider two events A and B, the conditional probability of the event A given that B has occurred is obtained as follows:
Find the probability that the business traveller will be on time in Los Angeles given that he arrives late in Chicago:
It is given that, a business traveller have to travel to Chicago in Cincinnati first and then board a connecting flight to Los Angeles.
The probability that Cincinnati based flight will be on time in Chicago is P(on time in Chicago) = 0.70.
The probability that Cincinnati based flight will be late in Chicago is P(late in Chicago) = 0.30.
The probability that the traveller be late in Chicago and on time in Los Angeles is P(late in Chicago and on time in Los Angeles) = 0.30
The probability that the business traveller will be on time in Los Angeles given that he arrives late in Chicago is obtained as 0.6667 from the calculation given below:
Answer:
The probability that the business traveller will be on time in Los Angeles given that he arrives late in Chicago is 0.6667.