Question

dalton is shopping for a new bicycle. he is most interested in color and type of tires. what is the probability that a randomly selected bike is green or has road bike tires? simplify any fractions.

Explanation:

Step1: Calculate the total number of bikes

We add up all the values in the table. \(5 + 6+4 + 5=20\)

Step2: Calculate the number of green bikes

The number of green bikes is \(4 + 5=9\)

Step3: Calculate the number of bikes with road - bike tires

The number of bikes with road - bike tires is \(5+4 = 9\)

Step4: Calculate the number of bikes that are green and have road - bike tires

The number of bikes that are green and have road - bike tires is \(4\)

Step5: Use the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)

Let \(A\) be the event that the bike is green and \(B\) be the event that the bike has road - bike tires.
\(P(A)=\frac{9}{20}\), \(P(B)=\frac{9}{20}\), \(P(A\cap B)=\frac{4}{20}\)
\(P(A\cup B)=\frac{9 + 9-4}{20}=\frac{14}{20}=\frac{7}{10}\)

Answer:

\(\frac{7}{10}\)