The probability that a pen from the first box and a crayon from the second box is selected is 7/24.
Given that,
A box contains 5 plain pencils and 7 pens.
A second box contains 5 color pencils and 5 crayons.
One item from each box is chosen at random.
We have to determine,
What is the probability that a pen from the first box and a crayon from the second box are selected?
According to the question
A box contains 5 plain pencils and 7 pens.
The probability of picking pens from the first box is,
[tex]\rm Probability \ of \ picking \ pen = \dfrac{Total\ number \ of \ pens}{Total \ number \ of \ pen \ and \ pencil}\\\\Probability \ of \ picking \ pen = \dfrac{7}{5+7}\\\\Probability \ of \ picking \ pen = \dfrac{7}{12}[/tex]
A second box contains 5 color pencils and 5 crayons.
The probability of picking crayon from the second box is,
[tex]\rm Probability \ of \ picking \ crayons = \dfrac{Total\ number \ of \ crayons}{Total \ number \ of \ crayons \ and \ color\ pencil}\\\\Probability \ of \ picking \ crayons = \dfrac{5}{5+5}\\\\Probability \ of \ picking \ crayons = \dfrac{5}{10}[/tex]
Therefore,
The probability that a pen from the first box and a crayon from the second box is selected is,
[tex]\rm = Probability \ of \ picking \ pens \times Probability \ of \ picking \ crayons \\\\= \dfrac{7}{12} \times \dfrac{5}{10}\\\\= \dfrac{35}{120}\\\\= \dfrac{7}{24}[/tex]
Hence, the probability that a pen from the first box and a crayon from the second box is selected is 7/24.
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