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Ivenika [448]
3 years ago
6

A box contains 5 plain pencils and 3 pens. A second box contains 3 color pencils and 9 crayons. One item from each box is chosen

at random. What is the
probability that a plain pencil from the first box and a color pencil from the second box are selected?
Write your answer as a fraction in simplest form.
Mathematics
1 answer:
Mars2501 [29]3 years ago
6 0
The probability of choosing a plain pencil from the first box is 5/8. The probability of choosing a color pencil from the second box is 3/12 which simplifies to 1/4. The probability of picking a plain pencil from the first box and picking a color pencil from the second box is 5/32 because 5/8 * 1/4 is 5/32

Final answer is 5/32 :)
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Bond [772]

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Subtracting this from the numerator gives a remainder of

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-x^3=-x\cdot x^2. Multiplying the denominator by -x gives

-x(x^2+2x+8)=-x^3-2x^2-8x

and subtracting this from the previous remainder gives a new remainder of

(-x^3-x^2-6x+8)-(-x^3-2x^2-8x)=x^2+2x+8

This last remainder is exactly the same as the denominator, so x^2+2x+8 divides through it exactly and leaves us with 1.

What we showed here is that

\dfrac{x^4+x^3+7x^2-6x+8}{x^2+2x+8}=x^2-\dfrac{x^3+x^2+6x-8}{x^2+2x+8}

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and this last expression is the quotient.

To verify this solution, we can simply multiply this by the original denominator:

(x^2+2x+8)(x^2-x+1)=x^2(x^2-x+1)+2x(x^2-x+1)+8(x^2-x+1)

=(x^4-x^3+x^2)+(2x^3-2x^2+2x)+(8x^2-8x+8)

=x^4+x^3+7x^2-6x+8

which matches the original numerator.

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