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

31.35%

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 = (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 = (5)/(16) }`

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

`\implies \mathsf{ (5)/(16) * 100 }`

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As a percent:

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