Phoenix is a hub for a large airline. Suppose that on a particular day, 8,000 passengers arrived in Phoenix on this airline. Phoenix was the final destination for 1,900 of these passengers. The others were all connecting to flights to other cities. On this particular day, several inbound flights were late, and 430 passengers missed their connecting flight. Of the 430, 95 were delayed overnight and had to spend the night in Phoenix. Consider the chance experiment of choosing a passenger at random from these 8,000 passengers. (Round your answers to three decimal places.)
(a) Compute the probability that the selected passenger had Phoenix as a final destination.
(b) Compute the probability that the selected passenger did not have Phoenix as a final destination.
(c) Compute the probability that the selected passenger was connecting and missed the connecting flight.
(d) Compute the probability that the selected passenger was a connecting passenger and did not miss the connecting flight.
(e) Compute the probability that the selected passenger ether had Phoens as a inal destination or was delayed overnight in Phoenix.

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joaobezerra joaobezerra · Answer 1 · 2021-02-26T01:25:10+01:00

Answer:

a) 0.238 = 23.8% probability that the selected passenger had Phoenix as a final destination.

b) 0.762 = 76.2% probability that the selected passenger did not have Phoenix as a final destination.

c) 0.054 = 5.4% probability that the selected passenger was connecting and missed the connecting flight.

d) 0.709 = 70.9% probability that the selected passenger was a connecting passenger and did not miss the connecting flight.

e) 0.249 = 24.9% probability that the selected passenger either had Phoenix as a initial destination or was delayed overnight in Phoenix.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

(a) Compute the probability that the selected passenger had Phoenix as a final destination.

1900 out of 8000 passengers. So

[tex]p = \frac{1900}{8000} = 0.238[/tex]

0.238 = 23.8% probability that the selected passenger had Phoenix as a final destination.

(b) Compute the probability that the selected passenger did not have Phoenix as a final destination.

8000 - 1900 = 6100 out of 8000 passengers. So

[tex]p = \frac{6100}{8000} = 0.762[/tex]

0.762 = 76.2% probability that the selected passenger did not have Phoenix as a final destination.

(c) Compute the probability that the selected passenger was connecting and missed the connecting flight.

430 out of 8000 passengers. So

[tex]p = \frac{430}{8000} = 0.054[/tex]

0.054 = 5.4% probability that the selected passenger was connecting and missed the connecting flight.

(d) Compute the probability that the selected passenger was a connecting passenger and did not miss the connecting flight.

6100 - 430 = 5670 out of 8000 passengers. So

[tex]p = \frac{5670}{8000} = 0.709[/tex]

0.709 = 70.9% probability that the selected passenger was a connecting passenger and did not miss the connecting flight.

(e) Compute the probability that the selected passenger either had Phoenix as a initial destination or was delayed overnight in Phoenix.

1900 initial, 95 delayed. So 1995 out of 8000.

[tex]p = \frac{1995}{8000} = 0.249[/tex]

0.249 = 24.9% probability that the selected passenger either had Phoenix as a initial destination or was delayed overnight in Phoenix.