Question

# Airline tickets can be purchased online, by telephone, or by using a travel agent. Passengers who...

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) = 0.80,

P(N) = 0.09,

and

P(ON) = 0.04.

(a)

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

-Yes, the events O and N are independent because P(ON) ≠ P(OP(N)

-Yes, the events O and N are independent because P(ON) = P(OP(N)

-No, the events O and N are not independent because P(ON) = P(OP(N)

-No, the events O and N are not independent because P(ON) ≠ P(OP(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 2 3 4
Not O 5 6 7
Total 8 9 1,000

(c)

Use the table to find P(ON):____

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.

Suppose

P(O) = 0.80,

P(N) = 0.09,

and

P(ON) = 0.04.

(a) Since P(ON) = 0.04 ≠P(O) .P(N)= 0.80*0.09=0.072 so the events O and N are not independent.

Hence Option: -No, the events O and N are not independent because P(ON) ≠ P(OP(N)

(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(ON)=P(O)+P(N)-P(ON) =800/1000+90/1000- 40/1000=0.85

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

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