Question

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?

Answer 1

We have:

x = total pens

n = number of black pens

so:

`x=6+4+8+n=18+n`

and for black pen:

`\begin{gathered} \frac{1}{10\text{ }}=0.1\text{ (probability)} \\ \text{then} \\ (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 \\ (0.9n)/(0.9)=(1.8)/(0.9) \\ n=2 \end{gathered}`

answer: 2 black pens