# University of Phoenix Week 3 Probability Trees Assignment Discussion

You fly from Philadelphia to San Francisco with a connection in Dallas. The probability that your flight from Philadelphia to Dallas arrives on time is 0.8. If you arrive on time, then the probability that your luggage makes the connection to San Francisco is 0.9. If you are delayed, then the probability that your luggage makes the connection with you is 0.5. In either case, you make the flight.

1. What is the probability that your luggage is there to meet you in San Francisco?

2. If your luggage is not there to meet you, what is the probability that you were late arriving in Dallas?

Please see if you can make a sketch to help solve this problem. The first branch consists of the probability of the flight from Philadelphia to Dallas On Time (.8) and the probability of the flight from Philadelphia to Dallas Not On Time (.2). Notice that these sum to a probability of 1. To find the probability of the various combinations, follow the branches and multiply the probabilities along the way.

Calculations:

P(Philadelphia to Dallas On Time and Luggage Arrives) = .8 x .9 = .72

P(Philadelphia to Dallas On Time and Luggage Does Not Arrive) = .8 x .1 = .08

P(Philadelphia to Dallas Not On Time and Luggage Arrives) = .2 x .5 = .10

P(Philadelphia to Dallas Not On Time and Luggage Does Not Arrive) = .2 x .5 = .10

Notice that these calculations all sum to 1, as we’ve covered all options. To get the final probability that the luggage is there to meet you, add .72 and .10 for a total probability of .82. These two are added together because in both cases, the luggage did arrive.

What are your thoughts on using a probability tree?

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