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$Some sanitation workers sifted through some recycling and trash to see whether people had correctly sorted their plastic bottles. Plastic #2 Plastic #4 Plastic #5 Correctly placed 5 7 7 Incorrectly placed 6 5 5 What is the probability that a randomly selected bottle is not correctly placed and is not made of plastic #2? Simplify any fractions. ◻$

Some sanitation workers sifted through some recycling and trash to see whether people had correctly sorted their plastic bottles. $\newline$ \begin{tabular}{|l|c|c|c|} $\newline$ \cline { $2$ - $4$ } & Plastic \# $2$ & Plastic \# $4$ & Plastic \# $5$ \\ $\newline$ \hline Correctly placed & $5$ & $7$ & $7$ \\ $\newline$ \hline Incorrectly placed & $6$ & $5$ & $5$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ What is the probability that a randomly selected bottle is not correctly placed and is not made of plastic \# $2$ ? $\newline$ Simplify any fractions. $\newline$ $\square$

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Probability of independent and dependent events

Full solution

Q. Some sanitation workers sifted through some recycling and trash to see whether people had correctly sorted their plastic bottles.

\newline

\begin{tabular}{|l|c|c|c|}

\newline

\cline {

2

-

4

} & Plastic \#

2

& Plastic \#

4

& Plastic \#

5

\\

\newline

\hline Correctly placed &

5

&

7

&

7

\\

\newline

\hline Incorrectly placed &

6

&

5

&

5

\\

\newline

\hline

\newline

\end{tabular}

\newline

What is the probability that a randomly selected bottle is not correctly placed and is not made of plastic \#

2

?

\newline

Simplify any fractions.

\newline

\square

Exclude Incorrect Plastic # $2$ Bottles: Now, we need to exclude the incorrectly placed Plastic # $2$ bottles from our count, since we're looking for bottles that are not correctly placed and not made of Plastic # $2$ . $\newline$ Incorrectly placed bottles that are not Plastic # $2$ : $16 - 6 = 10$ .
Find Total Bottles: Next, let's find the total number of bottles. $\newline$ Total bottles: $(5 + 6) + (7 + 5) + (7 + 5) = 11 + 12 + 12 = 35$ .
Calculate Probability: Finally, we calculate the probability. $\newline$ Probability = Number of incorrectly placed bottles that are not Plastic \# $2$ / Total number of bottles = $\frac{10}{35}$ . $\newline$ Simplify the fraction: $\frac{10}{35} = \frac{2}{7}$ .

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