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A box contains 6 red pens, 4 blue pens, 8 green pens, and some black pens. Leslie picks a pen and returns it to the box each time. the outcomes are: number of times a red pen is picked: 8number of times a blue pen is picked: 5 number of times a green pen is picked: 14number of times a black pen is picked: 3Question: if the theoretical probability of drawing a black pen is 1/10, how many black pens are in the box?

Respuesta :

We have:

x = total pens

n = number of black pens

so:

[tex]x=6+4+8+n=18+n[/tex]

and for black pen:

[tex]\begin{gathered} \frac{1}{10\text{ }}=0.1\text{ (probability)} \\ \text{then} \\ \frac{n}{18+n}=0.1 \\ n=0.1(18+n) \\ n=1.8+0.1n \\ n-0.1n=1.8+0.1n-0.1n \\ 0.9n=1.8 \\ \frac{0.9n}{0.9}=\frac{1.8}{0.9} \\ n=2 \end{gathered}[/tex]

answer: 2 black pens

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