P - Driving Risks Lesson

Driving Risks

Adapted from Course materials (II.A Student Activity Sheet 6 & 7) for AMDM developed under the leadership of the Charles A. Dana Center, in collaboration with the Texas Association of Supervisors of Mathematics and with funding from Greater Texas Foundation.

Probability can be used to help make decisions in everyday life. Few decisions are made with absolute certainty and in most cases, the decisions we make involve a degree of risk. Sometimes we are asked to make choices with several alternatives. The choice with the highest probability of success is usually the most favorable.

Jamal will be a high school senior next year. He wants to get a vehicle to celebrate his graduation. Jamal's mother researched vehicle safety and found that 1 of every 6 teenage drivers was involved in some kind of accident. While talking to his math teacher, Jamal mentioned that he did not think the risk was high enough to be concerned about. Jamal decided to survey 500 students, 230 of whom were male, to help him convince his mother to allow him to get a vehicle. No student has both a car and a motorcycle.

 

Using the data, what is the probability that Jamal will be involved in an accident if he gets a motorcycle?

Of the 23 males who had a motorcycle, 6 were involved in an accident. Therefore, the probability is 26%.

Based on these survey data, Jamal told his mother that he only has a 1% chance of getting in an accident. Is he correct? Why or why not?

Jamal is not correct. He used the entire sample size of 500 instead of limiting his math to those students who were boys or who had vehicles. He also only used the number of accidents for motorcycles, the least number of collisions! Using these numbers, his chance of an accident is only 1.2%.

 

The more accurate sample to use is boys who have cars. If he does get a car, his chance of getting in an accident is closer to 27%

 

You do this one. 

What is his chance of having an accident if he gets a motorcycle?

6/23 =.26 0.26 x 100 = 26%

If he gets either a car or a motorcycle, his chance of getting in an accident is 26.6%

 

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