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An airline offers discounted "advance-purchase" fares to customers who buy tickets more than 30 days before travel and charges "regular" fares for tickets purchased during those last 30 days. The company has noticed that $60 \%$ of its customers take advantage of the advance-purchase fares. The "no-show" rate among people who paid regular fares is $30 \%,$ but only $5 \%$ of customers with advance-purchase tickets are no-shows. a. What percent of all ticket holders are no-shows? b. What's the probability that a customer who didn't show had an advance-purchase ticket? c. Is being a no-show independent of the type of ticket a passenger holds? Explain.

   An airline offers discounted "advance-purchase" fares to customers who buy tickets more than 30 days before travel and charges "regular" fares for tickets purchased during those last 30 days. The company has noticed that $60 \%$ of its customers take advantage of the advance-purchase fares. The "no-show" rate among people who paid regular fares is $30 \%,$ but only $5 \%$ of customers with advance-purchase tickets are no-shows.
a. What percent of all ticket holders are no-shows?
b. What's the probability that a customer who didn't show had an advance-purchase ticket?
c. Is being a no-show independent of the type of ticket a passenger holds? Explain.

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Stats Data and Models

Stats Data and Models

Richard D. De Veaux,… 5th Edition

Chapter 13, Problem 56

Instant Answer

Step 1

Plugging in the given values, we get: (0.60 * 0.05) + (0.40 * 0.30) = 0.03 + 0.12 = 0.15 So, 15% of all ticket holders are no-shows. b. Show more…

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Transcript

00:02 For this question, we still use the tree diagram to help us to understand the whole process.

00:08 And here we know from the question that if a custom choose the advanced purchase, yes.

00:24 Yes means choose the advanced purchase.

00:27 No means didn't use the advance purchase.

00:30 And we know 60 % of the custom choose this service.

00:35 So here is 0 .6, which means the no advance purchase is 0 .4.

00:44 And for those who choose advanced purchase, the no show rate is only 0 .05%, but for those who didn't choose the advance purchase, the no show rate is only 0 .05 .5%.

01:05 But for those who didn't choose the advance purchase, the no show rate is 30%.

01:15 0 .3 and we can use this to finish the whole tray.

01:21 The shoe rate here should be 0 .95.

01:26 The shoot rate for those who didn't choose advanced purchase is 0 .7.

01:34 Question a is to calculate the percent of all custom on no show.

01:44 So probability no show.

01:45 So probability no show has two components.

01:51 First one is the probability that the custom choose the advance purchase and no show.

02:00 Plus, the custom didn't choose the advanced purchase and no show.

02:10 Plug in the number.

02:12 The first one is 0 .6 times 0 .95.

02:22 Oh, sorry.

02:27 Since it's no show, we should use 0 .6 .9 .5...

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