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Natalie works at a store where she must choose 1 item from each of the following options: a sweater or a blouse; a brown pair of pants, a black pair of pants, or a skirt; and a pair of sandals or boots.

The following tree diagram shows the possible outcomes.


A 3-column tree diagram: top, bottom, & shoes. Top column shows sweater & blouse, & each branches to pants probability 2 thirds & skirt 1 third. Each pants & skirt branch to sandals & boots.



What is the probability of randomly selecting an outfit that is a sweater, pants, and boots?

Enter your answer as a reduced fraction, like this: 3/14

Answer :

Using it's concept, it is found that there is a [tex]\frac{1}{6}[/tex] probability of randomly selecting an outfit that is a sweater, pants, and boots.

What is a probability?

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

Researching the problem on the internet, we have that:

  • There is a 1/2 probability of choosing a sweater.
  • With a sweater, there is a 2/3 probability of choosing pants.
  • With pants, there is a 1/2 probability of choosing boots.

Considering these events are independent, the probability is given by:

[tex]p = \frac{1}{2} \times \frac{2}{3} \times \frac{1}{2} = \frac{1}{6}[/tex]

More can be learned about probabilities at https://brainly.com/question/14398287

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