Question

Traffic data revealed that 35 percent of automobiles traveling along a portion of an interstate highway were exceeding the legal speed limit. using highway cameras and license plate registrations, it was also determined that 52 percent of sports cars were also speeding along the same portion of the highway. what is the probability that a randomly selected car along the same portion of the highway was a speeding sports car?

Answer 1

The probability that a randomly selected car along the same portion of the highway was a speeding sports car $\boxed{0.182{\text{ or 18}}{\text{.2\%}}}$.

Further Explanation:

The independent probabilities of two sets can be calculated as follows,

$\boxed{P\left({A \cap B}\right)=P\left(A\right)\times P\left(B\right)}$.

Here, A represents the first event and B represents the second event.

Given:

In traffic data there are 35 percent of automobiles.

There 52 percent of sports cars that are speeding on the highway.

Calculation:

Let A denote the event that a vehicle travelling on the highway is an automobile.

The probability of event A can be calculated as follows,

$\begin{aligned}P\left(A\right)&=35\%\\&=0.35\\\end{aligned}$

Let B denote the event that an automobile is a speeding sports car.

The probability of event B can be calculated as follows,

$\begin{aligned}P\left(B\right)&=52\%\\&=0.52\\\end{aligned}$

The probability that a randomly selected car along the same portion of the highway was a speeding sports car can be calculated as follows,

$\begin{aligned}{\text{Probability}}&=0.52\times0.35\\&=0.182\\\end{aligned}$

The probability that a randomly selected car along the same portion of the highway was a speeding sports car $\boxed{0.182{\text{ or 18}}{\text{.2\%}}}$.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Traffic data, automobiles, 35 percent, travelling, same proportion, probability, sports car, normal car, speeding sports car, highway, license, plate registration, speed limit, exceeding, legal, interstate highway, percent, cameras.

Answer 2

This is a typo and vaguely phrased. However, the closest to a direct solution is to think of it as follows: 35% of the cars are speeding. Out of these, 52% of the cars are also speeding. Hence, the result of cars that are both speeding and speed cars is 0.52*0.35=0.182