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Travel agents collected data from recent travelers about their modes of transportation for their vacations, They found that 37% traveled by airplane, 8% traveled by train, and 7% traveled by airplane and train. Let A be the event that the mode of travel was airplane and let T be the event that the mode of travel was train.​

Travel agents collected data from recent travelers about their modes of transportation for their vacations They found that 37 traveled by airplane 8 traveled by class=

Respuesta :

Using Venn probabilities, it is found that the probability is [tex]P(A \cap T^{c}) = 0.3[/tex]

In this problem, the events are:

  • Event A: Traveled by airplane.
  • Event T: Traveled by train.
  • Event [tex]T^{c}[/tex]: Did not travel by train.

The desired probability is:

[tex]P(A \cap T^{c}) = P(A) + P(T^{c}) - P(A \cup T^{c})[/tex]

The probabilities are:

  • 37% traveled by airplane, hence [tex]P(A) = 0.37[/tex]
  • 8% traveled by train, hence [tex]P(T^c) = 1 - 0.08 = 0.92[/tex]
  • 37% traveled by airplane, 62%(100 - [37 + 8 - 7]) did not travel, hence [tex]P(A \cup T^c) = 0.37 + 0.62 = 0.99[/tex]

Then:

[tex]P(A \cap T^{c}) = P(A) + P(T^{c}) - P(A \cup T^{c})[/tex]

[tex]P(A \cap T^{c}) = 0.37 + 0.92 - 0.99[/tex]

[tex]P(A \cap T^{c}) = 0.3[/tex]

A similar problem is given at https://brainly.com/question/24707032

Answer:

B: .30

Step-by-step explanation:

edg 2021

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