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$Suzie is shopping for a new bicycle. She is most interested in color and type of tires. Red Green Road bike tires 5 9 Mountain bike tires 6 7 City bike tires 8 7 What is the probability that a randomly selected bike does not have mountain bike tires and is not red? Simplify any fractions. ◻$

Suzie is shopping for a new bicycle. She is most interested in color and type of tires. $\newline$ \begin{tabular}{|l|c|c|} $\newline$ \hline & Red & Green \\ $\newline$ \hline Road bike tires & $5$ & $9$ \\ $\newline$ \hline Mountain bike tires & $6$ & $7$ \\ $\newline$ \hline City bike tires & $8$ & $7$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ What is the probability that a randomly selected bike does not have mountain bike tires and is not red? $\newline$ Simplify any fractions. $\newline$ $\square$

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Probability of independent and dependent events

Full solution

Q. Suzie is shopping for a new bicycle. She is most interested in color and type of tires.

\newline

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

\newline

\hline & Red & Green \\

\newline

\hline Road bike tires &

5

&

9

\\

\newline

\hline Mountain bike tires &

6

&

7

\\

\newline

\hline City bike tires &

8

&

7

\\

\newline

\hline

\newline

\end{tabular}

\newline

What is the probability that a randomly selected bike does not have mountain bike tires and is not red?

\newline

Simplify any fractions.

\newline

\square

Total Bikes Calculation: Total number of bikes = $5$ (Red Road) + $9$ (Green Road) + $6$ (Red Mountain) + $7$ (Green Mountain) + $8$ (Red City) + $7$ (Green City) = $42$ bikes.
Non-Red Bikes Count: Number of bikes that are not red = $9$ (Green Road) + $7$ (Green Mountain) + $7$ (Green City) = $23$ bikes.
Non-Mountain Tires Count: Number of bikes that do not have mountain bike tires = $5$ (Red Road) + $9$ (Green Road) + $8$ (Red City) + $7$ (Green City) = $29$ bikes.
Non-Red Non-Mountain Bikes Count: Number of bikes that are not red and do not have mountain bike tires = $9$ (Green Road) + $7$ (Green City) = $16$ bikes.
Probability Calculation: Probability = $\frac{\text{Number of bikes that are not red and do not have mountain bike tires}}{\text{Total number of bikes}}$ = $\frac{16}{42}$ .
Fraction Simplification: Simplify the fraction $\frac{16}{42}$ by dividing both numerator and denominator by $2 = \frac{8}{21}$ .

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