Question

A box contains 6 black pens, 4 blue pens, and 7 red pens. Without looking, Clarissa randomly picks a black pen out of the box. If she chooses another pen out of the box without replacing the first one, what is the probability that she will pick a black pen both times? Write your answer as a percent.
Group of answer choices

Answer 1

Answer:

31.35%

Step-by-step explanation:

Initial reading:

In the box, there are:

• 6 Black pens
• 4 blue pens
• 7 red pens

Total number of pens in the box = 6 + 4 + 7

= 17

If we count pens as outcomes the total number of possible outcomes are 17.

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New reading:

Clarissa takes out a black pen from the box.

That reduces the number of black pens by 1 which increases the total number of pens by 1 as well.

So now:

• Number of black pens = 6 - 1 = 5
• Total number of pens = 17 - 1 = 16

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Probability:

$\boxed{ \mathsf{probability = \frac{favorable \: outcomes}{total \: outcomes} }}$

If we want her to pick up a black pen, and she ends up picking one. So, we can say that the outcome is in our favor.

That makes it,

• the number of favorable outcomes = number of black pens

= 5

• and total outcomes = Total number of pens

= 16

$\implies\mathsf{probability = \frac{5}{16} }$

For showing it as some percent we'll just multiply the fraction by 100

$\implies \mathsf{ \frac{5}{16} \times 100 }$

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As a percent:

$\implies \mathsf{ \underline{ 31.25 \: \% } }$