Question

Airline tickets can be purchased online, by telephone, or by using a travel agent. Passengers who have a ticket sometimes don't show up for their flights. Suppose a person who purchased a ticket is selected at random. Consider the following events. O = event selected person purchased ticket online N = event selected person did not show up for flight Suppose P(O) = 0.70, P(N) = 0.09, and P(O ∩ N) = 0.04. (a) Are the events N and O independent? How can you tell? No, the events O and N are not independent because P(O ∩ N) ≠ P(O)·P(N) (b) Construct a hypothetical 1,000 table with columns corresponding to N and not N and rows corresponding to O and not O. N Not N Total O 40 660 700 Not O 50 250 300 Total 90 910 1000 (c) Use the table to find P(O ∪ N). Give a relative frequency interpretation of this probability. P(O ∪ N) = (40 + 660 + 50) / 1000 = 750 / 1000 = 0.75 In the long run, 75% of airline ticket purchasers will buy their ticket online or not show up for a flight, or both.

          Airline tickets can be purchased online, by telephone, or by using a travel agent. Passengers who have a ticket sometimes don't show up for their flights. Suppose a person who purchased a ticket is selected at random. Consider the following events.

O = event selected person purchased ticket online
N = event selected person did not show up for flight

Suppose P(O) = 0.70, P(N) = 0.09, and P(O ∩ N) = 0.04.

(a) Are the events N and O independent? How can you tell?

No, the events O and N are not independent because P(O ∩ N) ≠ P(O)·P(N)

(b) Construct a hypothetical 1,000 table with columns corresponding to N and not N and rows corresponding to O and not O.

        N     Not N   Total
O     40      660     700
Not O 50      250     300
Total 90      910     1000

(c) Use the table to find P(O ∪ N). Give a relative frequency interpretation of this probability.

P(O ∪ N) = (40 + 660 + 50) / 1000 = 750 / 1000 = 0.75

In the long run, 75% of airline ticket purchasers will buy their ticket online or not show up for a flight, or both.

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Added by Richard M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert David Nguyen

10/21/2022

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Step 1: Calculate the probability of the union of events O and N using the table provided. Show more…

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Airline tickets can be purchased online, by telephone, or by using a travel agent. Passengers who have a ticket sometimes don't show up for their flights. Suppose a person who purchased a ticket is selected at random. Consider the following events. O = event selected person purchased ticket online N = event selected person did not show up for flight Suppose P(O) = 0.70, P(N) = 0.09, and P(O ∩ N) = 0.04. (a) Are the events N and O independent? How can you tell? No, the events O and N are not independent because P(O ∩ N) ≠ P(O)·P(N) (b) Construct a hypothetical 1,000 table with columns corresponding to N and not N and rows corresponding to O and not O. N Not N Total O 40 660 700 Not O 50 250 300 Total 90 910 1000 (c) Use the table to find P(O ∪ N). Give a relative frequency interpretation of this probability. P(O ∪ N) = (40 + 660 + 50) / 1000 = 750 / 1000 = 0.75 In the long run, 75% of airline ticket purchasers will buy their ticket online or not show up for a flight, or both.

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Transcript

00:01 Hi, i'm david and i'm hager hamill and send your question.

00:02 Now let me bring up your question here.

00:05 In the question here, we summarize the question pen notation.

00:09 Well, we have the event o denoted by the person purchased the ticket online.

00:16 And we are given the probability of the o equal to 0 0 0 0 .70.

00:22 The end will be event that the person did not show up on ffundafly, equal to the 0 .09.

00:28 And then the probability of and n equal to the zepon 0 4.

00:41 Now in the first question a we need to see if n and o are independent.

00:49 We see that it will try to find the probability of o times of probability n equal to the 07 times in the zobon 0 9.

00:59 Then we get equal to the zobon 063 and it's not the same as a zabon 0 4 which is the probability of the o and n, therefore the o and n are not independent.

01:24 And then the right answer here it will be the answer will be no.

01:29 Here it will be no because even independent.

01:35 It will be the right one are not independent because probability only are not equal.

01:40 Then the next one we need to construct the table with the 100 sample.

01:45 So we will have the table here where we have this will be, this one will be for the o.

01:56 So this will be the event o and then this will be the not only will put the o bar and then the other one will be the end and then this will be not end will be the end bar and we have the total equal to the 1000.

02:18 Now we have to fill up here.

02:20 So we have the probability the o equals to the 017.

02:24 It means that this quantity here will be, we turn the 1000 times from the 017 equal to the 700.

02:31 The remaining will be the 1000 times 013 equal to the 300...

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