
Men versus Women Drivers
The higher probability that women will have an automobile accident contributes to an increase in the accident rate for men. To determine exactly how much higher the accident rate for men is because of women drivers it is necessary to calculate the rate per one million miles that both men and women are expected to have an accident. If we let N_{m} be the number of accidents per million miles that a man is expected have an auto accident, and N_{f }that a woman will, then we have two equations and two variables. The total number of accidents per million miles that a man is expected to have an accident, R_{m}, is the sum of his likelihood per million miles of having a single driver accident N_{m}, the square of this probability to represent a two driver accident involving another man N_{m}^{2}, and the N_{m} times N_{f} to represent a two driver accident involving a woman: (N_{m} + N_{m}^{2} + N_{m}N_{f}) x 965 billion miles driven = 2,418,799 accidents R_{m} = N_{m} + N_{m}^{2} + N_{m}N_{f }= 2.5 The equation for women is similar: (N_{f} + N_{f}^{2} + N_{m}N_{f}) x 513 billion miles driven = 1,701,043 accidents R_{f} = N_{f} + N_{f}^{2} + N_{m}N_{f} = 3.32 N_{m} = (3.32  N_{f}  N_{f}^{2})/N_{f} (3.32  N_{f } N_{f}^{2})/N_{f} + (11.0224 6.64N_{f}  5.64N_{f}^{2} + 2N_{f}^{3} + N_{f}^{4} )/N_{f}^{2} + 3.32 N_{f}^{ }N_{f}^{2} = 2.5 3.32N_{f } N_{f}^{2}  N_{f}^{2} + 11.0224 6.64N_{f}  5.64N_{f}^{2} + 2N_{f}^{3} + N_{f}^{4} + 3.32N_{f}^{2 } N_{f}^{3  }N_{f}^{4 = 2.5}N_{f}^{2} 3.32N_{f}^{ }+ 5.82N_{f}^{2} = 11.0224 N_{f}^{ }= 1.087 = The number of accidents per million miles that that a woman is expected to have. N_{m}^{ }= 0.213 = The number of accidents per million miles that that a man is expected to have. N_{f}^{ }= 5.1 x N_{m} If all drivers were men who drove the 1,478 billion miles which are currently driven by both men and women, the total accident rate would be 0.26 accidents per million miles, for a total of 380,480 accidents: (N_{m} + N_{m}^{2}) x 1,478,000 million miles = 381,869 accidents If all drivers were women who drove the 1,478 billion miles which are currently driven by both men and women, the total accident rate would be 2.27 accidents per million miles, for a total of 3,352,945 accidents: (N_{f} + N_{f}^{2}) x 1,478,000 million miles = 3,352,945 accidents If only men drove today, accidents would decrease from 2,059,921 to 380,480 per year, a reduction of 81%. If only women drove, accidents would increase from 2,059,921 to 3,352,945 per year, a 63% increase and there would be 8.8 times as many accidents as if only men drove. Women who have accidents with men increase men's overall accident rate per million miles from 0.26 to 2.5, an increase of 860%. If only men drove all 1,478 billion miles currently driven by both men and women, the annual economic loss to automobile accidents would be between $121.5 billion of the $150 billion less, and 36,450 of the 45,000 lives currently lost each year to auto accidents would be saved. Over the next two decades, this is $23 trillion and 730,000 lives, not considering population growth.
REFERENCES:
The National Transportation Survey reports that women drive only 30% of the miles driven, and men 70%. The actual percent of drivers involved in fatal traffic collisions reported by the Fatal Accident Reporting System which are women is 37.4%, versus 62.6% which are men. If these figures are correct, then the fatal accident rate for women is higher than in the above references. 

