What is the Probability of a Delayed Flight Given Luggage Arrived in Vancouver?

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Homework Help Overview

The problem involves calculating the probability of a delayed flight given that luggage has arrived in Vancouver. It centers around conditional probabilities related to flight schedules and luggage handling during connections.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the definitions of events A and B, questioning their independence. There is an exploration of the probabilities associated with on-time and delayed flights and their impact on luggage arrival.

Discussion Status

Some participants are attempting to clarify their understanding of the problem and the underlying probabilities. There is a recognition of the complexity of the situation, with one participant reflecting on their initial overthinking of the problem.

Contextual Notes

The original poster expresses uncertainty about the teacher's provided answer and the calculations leading to it. There is a mention of a specific numerical answer (0.17) without further elaboration on how it was derived.

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Homework Statement


Suppose Sarah is flying from Regina to Vancouver with a connection in Edmonton. The probability that her first flight leaves on time is 0.77. If the first flight is on time, the probability that her luggage will make the connection flight in Edmonton is 0.92. But if the first flight is delayed, the probability that the luggage will make it is only 0.63.

Suppose that her luggage arrived in Vancouver with her, what is the probability that the fist flight was delayed?

The answer for this is 0.17, but I'm not sure how our teacher got this.

Homework Equations


[itex]P(A|B) = \frac{P(A\cap B)}{P(B)}[/itex]

[itex]P(A\cap B)=P(A)P(B|A)=P(B)P(A|B)[/itex]

The Attempt at a Solution


I found that the probability her luggage arrives in Vancouver with her is 0.8533.

I drew the following:

Probability first flight leaves on time: 0.77
- Probability baggage arrives: 0.92
- Probability baggage does not arrive: 0.04
Probability first flight leaves late: 0.23
- Probability baggage arrives: 0.63
- Probability baggage does not arrive: 0.370

I thought that [itex]P(A\cap B)=0[/itex] so then [itex]P(A)P(B|A)=P(B)P(A|B)=0[/itex] but this doesn't seem as if it could be true...
 
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What events do A and B represent, and are these independent events?
 
PirateFan308 said:

Homework Statement


Suppose Sarah is flying from Regina to Vancouver with a connection in Edmonton. The probability that her first flight leaves on time is 0.77. If the first flight is on time, the probability that her luggage will make the connection flight in Edmonton is 0.92. But if the first flight is delayed, the probability that the luggage will make it is only 0.63.

Suppose that her luggage arrived in Vancouver with her, what is the probability that the fist flight was delayed?

The answer for this is 0.17, but I'm not sure how our teacher got this.

Homework Equations


[itex]P(A|B) = \frac{P(A\cap B)}{P(B)}[/itex]

[itex]P(A\cap B)=P(A)P(B|A)=P(B)P(A|B)[/itex]

The Attempt at a Solution


I found that the probability her luggage arrives in Vancouver with her is 0.8533.

I drew the following:

Probability first flight leaves on time: 0.77
- Probability baggage arrives: 0.92
- Probability baggage does not arrive: 0.04
Probability first flight leaves late: 0.23
- Probability baggage arrives: 0.63
- Probability baggage does not arrive: 0.370

I thought that [itex]P(A\cap B)=0[/itex] so then [itex]P(A)P(B|A)=P(B)P(A|B)=0[/itex] but this doesn't seem as if it could be true...

What do A and B represent in this case?

Sometimes (not always) people find it easier to think about such problems in the following manner: imagine that Sarah makes the trip 10,000 times. In how many trips is her first flight on time? How many times late? For all the on-time trips, in how many does her luggage arrive? For all the late trips, in how many does her luggage arrive? Now look at all the cases in which her luggage arrives. In how many of those was the first flight on time?

RGV
 
Last edited:
Wow, I really over thought that. Thanks!
 
sorry didn't mean to submit, only meant to use to view this other post with latex correctly. There's no delete button?