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7. Jackie has one red pencil, one yellow pencil, one blue pencil,
one green pencil, one orange pencil, and one purple pencil. She
also has one red pen, one blue pen, and one black pen. If Jackie
randomly selects one pencil and one pen, what is the probability
that she will select a purple pencil and a black pen in that order?

Respuesta :

jkakeller

Answer:

I believe it is 1/6 for the pencil and 1/3 for the pen. Altogether, 2/9.

Step-by-step explanation:

There is 1 purple pencil out of 6 and 1 black pen out of 3.

Using probability of independent events, it is found that there is a [tex]\frac{1}{15}[/tex] probability  that she will select a purple pencil and a black pen in that order.

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

If two events, A and B, are independent, the probability of both happening is the multiplication of the probabilities of each happening, that is:

[tex]P(A \cap B) = P(A)P(B)[/tex]

In this question:

  • The pencil and the pen are independent.
  • One of the five pencils are purple, thus [tex]P(A) = \frac{1}{5}[/tex].
  • One of the three pens are black, thus [tex]P(B) = \frac{1}{3}[/tex].

The probability is:

[tex]P(A \cap B) = P(A)P(B) = \frac{1}{5} \times \frac{1}{3} = \frac{1}{15}[/tex]

[tex]\frac{1}{15}[/tex] probability  that she will select a purple pencil and a black pen in that order.

A similar problem is given at https://brainly.com/question/23855473

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