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*(

* P*(

and

* P*(

(a)

Are the events *N* and *O* independent? How can
you tell?

-Yes, the events O and N are independent because
* P*(

-Yes, the events O and N are independent because
* P*(

-No, the events O and N are not independent because
* P*(

-No, the events O and N are not independent because
* P*(

(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 | 2 | 3 | 4 |

Not O | 5 | 6 | 7 |

Total | 8 | 9 | 1,000 |

(c)

Use the table to find * P*(

Give a relative frequency interpretation of this probability.

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

Answer #1

Suppose

* P*(

* P*(

and

* P*(

(a) Since * P*(

Hence Option: -No, the events O and N are not independent
because * P*(

(b)

N | Not N | Total | |
---|---|---|---|

O | 0.04*1000=40 | 800-40=760 | 0.80*1000=800 |

Not O | 90-40=50 | 910-760=150 | 1000-800=200 |

Total | 0.09*1000=90 | 1000-90=910 | 1,000 |

(c)

* P*(

In the long run, 85% of airline ticket purchasers will buy their ticket online or not show up for a flight, or both.

In this exercise we examine the effects of overbooking in the
airline industry. Ontario Gateway Airlines' first class cabins have
10 seats in each plane. Ontario's overbooking policy is to sell up
to 11 first class tickets, since cancellations and no-shows are
always possible (and indeed are quite likely). For a given flight
on Ontario Gateway, there were 11 first class tickets sold. Suppose
that each of the 11 persons who purchased tickets has a 20% chance
of not showing...

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True
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