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$Dalton is shopping for a new bicycle. He is most interested in color and type of tires. Road bike tires Mountain bike tires Red 5 6 Green 4 5 What is the probability that a randomly selected bike is green or has road bike tires? Simplify any fractions. ◻$

Dalton is shopping for a new bicycle. He is most interested in color and type of tires. $\newline$ \begin{tabular}{|l|c|c|} $\newline$ \hline Road bike tires & Mountain bike tires \\ $\newline$ \hline Red & $5$ & $6$ \\ $\newline$ \hline Green & $4$ & $5$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ What is the probability that a randomly selected bike is green or has road bike tires? $\newline$ Simplify any fractions. $\newline$ $\square$

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Theoretical probability

Full solution

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

\newline

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

\newline

\hline Road bike tires & Mountain bike tires \\

\newline

\hline Red &

5

&

6

\\

\newline

\hline Green &

4

&

5

\\

\newline

\hline

\newline

\end{tabular}

\newline

What is the probability that a randomly selected bike is green or has road bike tires?

\newline

Simplify any fractions.

\newline

\square

Count Total Bikes: Count the total number of bikes. Add up all the bikes in the table. $\newline$ $5$ (Red Road) + $6$ (Red Mountain) + $4$ (Green Road) + $5$ (Green Mountain) = $20$ bikes total.
Count Green Bikes: Count the number of green bikes. Add the green road bikes to the green mountain bikes. $\newline$ $4$ (Green Road) + $5$ (Green Mountain) = $9$ green bikes.
Count Road Bikes: Count the number of bikes with road bike tires. Add the red road bikes to the green road bikes. $\newline$ $5$ (Red Road) + $4$ (Green Road) = $9$ road bikes.
Calculate Probability: Calculate the probability of selecting a green bike or a bike with road tires. Since some bikes are both green and have road tires, we need to subtract the overlap to avoid double-counting. $\newline$ $P(\text{Green or Road Tires}) = P(\text{Green}) + P(\text{Road Tires}) - P(\text{Green and Road Tires})$ $\newline$ $P(\text{Green or Road Tires}) = \frac{9}{20} + \frac{9}{20} - \frac{4}{20}$
Simplify Fraction: Simplify the fraction. $P(\text{Green or Road Tires}) = \frac{9 + 9 - 4}{20} = \frac{14}{20}$
Reduce Fraction: Reduce the fraction to its simplest form. $\frac{14}{20}$ can be simplified to $\frac{7}{10}$ by dividing both the numerator and the denominator by $2$ .

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