Students who take drivers education have a 3% probability of having an accident in their first year of driving,while students who do not take drivers education have a 9% probability.Statistics show that the average cost of an accident is $7000.Statistics also show that x% of new drivers have taken drivers education.If the expected cost of an accident per driver in their first year of driving is $394.80,what is the value of x?
A)56%
B)53%
C)47%
D)44%

Question

Quizplus · Accepted Answer

The expected cost of an accident per driver can be calculated using the formula: Expected Cost = (Probability of Accident for Educated Drivers * Cost of Accident * Percentage of Educated Drivers) + (Probability of Accident for Non-Educated Drivers * Cost of Accident * Percentage of Non-Educated Drivers). Given that the expected cost is $394.80, the cost of an accident is $7000, the probability of an accident for educated drivers is 3% (or 0.03), and for non-educated drivers is 9% (or 0.09), we can set up the equation: 394.80 = (0.03 * 7000 * x) + (0.09 * 7000 * (1-x)), where x is the percentage of new drivers who have taken driver's education. Solving for x gives us 56%.

Students Who Take Drivers Education Have a 3% Probability of Having