The higher probability that women will have an 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
probability for both men and women to have an accident. If we let P_{m} be
the probability that a man will have an auto accident, and P_{f }that a woman
will, then we have two equations and two variables. The total probability that a man
will have an accident is the sum of his probability of having a single driver accident,
the square of this probability to represent a two driver accident involving another man,
and the P_{m} times P_{f} to represent a two driver accident
involving a woman:

(P_{m} + P_{m}^{2} + P_{m}P_{f})
x 965,000 million miles driven = 2,418,799 accidents

P_{m} + P_{m}^{2} + P_{m}P_{f
}= 2.5

The equation for women is similar:

(P_{f} + P_{f}^{2} + P_{m}P_{f})
x 513,000 million miles driven = 1,701,043 accidents

P_{f} + P_{f}^{2} + P_{m}P_{f}
= 3.32

P_{m} = (3.32 - P_{f} -
P_{f}^{2})/P_{f}

(3.32 - P_{f }- P_{f}^{2})/P_{f} + (11.0224 -6.64P_{f}
- 5.64P_{f}^{2} + 2P_{f}^{3}
+ P_{f}^{4} )/P_{f}^{2}
+ 3.32 -P_{f}^{ -}P_{f}^{2} =
2.5

3.32P_{f }- P_{f}^{2}
- P_{f}^{2} + 11.0224 -6.64P_{f} - 5.64P_{f}^{2}
+ 2P_{f}^{3} + P_{f}^{4}
+ 3.32P_{f}^{2 -} P_{f}^{3 - }P_{f}^{4
= 2.5}P_{f}^{2}

3.32P_{f}^{ }+ 5.82P_{f}^{2} =
11.0224

P_{f}^{ }= 1.087 = Probability that a woman will
have an auto accident

P_{m}^{ }= 0.213 = Probability that a man will have
an auto accident

P_{f}^{ }= 5.1 x P_{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:

(P_{m} + P_{m}^{2})
x 1,478,000 = 380,480 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 2.271 accidents per million miles,
for a total of 3,352,945 accidents:

(P_{f} + P_{f}^{2})
x 1,478,000 = 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 than if
only men drove.

Women drivers are thus responsible for $121.5 billion of the $150 billion annual
economic loss and 36,450 of the 45,000 lives lost each year to auto accidents.

A = Drinking men = 11 = A + A^{2} + AB + AC + AD

B = Drinking women = 6 = B + B^{2} + AB + AC + AD

C = Non-drinking men = 47 = C + C^{2} + AC + AB + AD

D = Non-drinking women = 75 = D + D^{2} + AD + BD +
CD

B = (47 - C - C^{2} - AC - AD)/A

D = (11 - A - A^{2} - AB - AC)/A

A = (75 - D - D^{2} - BD - CD)/D

B = (47 - C - C^{2} - (75C - CD -CD^{2} - BCD - C^{2}D)/D - 75 - D -
D^{2} - BD - CD)/ (75 - D - D^{2}
- BD - CD)/D

B = (47D - CD - C^{2}D - 75C - CD -CD^{2} - BCD - C^{2}D - 75D - D^{2} - D^{3} - BD^{2} - CD^{2})/ (75 - D - D^{2} - BD - CD)

75B - BD - BD^{2} - B^{2}D
- BCD = 47D - CD - C^{2}D - 75C - CD -CD^{2} - BCD - C^{2}D - 75D - D^{2} - D^{3} - BD^{2} - CD^{2}

75B - BD - 0BD^{2} - B^{2}D - 0BCD +28D +2CD +2C^{2}D
-75C +0CD^{2} +D^{2}
+D^{3} = 0

75B - BD - B^{2}D +28D +2CD
+2C^{2}D -75C +D^{2}
+D^{3} = 0

A^{2} = (5625 - 150D - 149D^{2}
- 150DB +2D^{3} -150DC +2D^{2}B
+ D^{4} +2D^{3}B + 2D^{2}C + 2D^{3}C + D^{2}B^{2} +2D^{2}BC +D^{2}C^{2})/D^{2}

11 = (75 - D - D^{2} - BD - CD)/D + (5625 - 150D -
149D^{2} - 150DB +2D^{3}
-150DC +2D^{2}B + D^{4}
+2D^{3}B + 2D^{2}C +
2D^{3}C + D^{2}B^{2} +2D^{2}BC +D^{2}C^{2})/D^{2} + (75B - BD - BD^{2}
- B^{2}D - BCD)/D + (75C - CD - CD^{2} - CBD - C^{2}D)/D + 75
- D - D^{2} - BD - CD

11D^{2} = 75D - D^{2}
- D^{3} - BD^{2} - CD^{2} + 5625 - 150D - 149D^{2} -
150DB +2D^{3} -150DC +2D^{2}B
+ D^{4} +2D^{3}B + 2D^{2}C + 2D^{3}C + D^{2}B^{2} +2D^{2}BC +D^{2}C^{2}
+ 75BD - BD^{2} - BD^{3}
- B^{2}D^{2} - BCD^{2} + 75CD - CD^{2} - CD^{3} - CBD^{2} - C^{2}D^{2} + 75D^{2} - D^{3} - D^{4} - BD^{3} - CD^{3}

5625 -75D - 86D^{2} + 0D^{3}
- 0BD^{2} -75BD -75CD +0D^{4}
+ 0D^{3}B + 0CD^{2}
+0D^{3}C +0D^{2}B^{2} + 0D^{2}BC +0D^{2}C^{2} - 0CD^{3}
= 0

5625 -75D - 86D^{2} -75BD -75CD = 0

75BD = 5625 -75CD -75D - 86D^{2}

B = (5625 -75CD -75D - 86D^{2})/75D

A = (75 - D - D^{2} - BD - CD)/D

A = (75 - D - D^{2} - ((5625 -75CD -75D - 86D^{2})/75) - CD)/D

A = (5625 - 75D - 75D^{2} - 5625 +75CD +75D + 86D^{2} - 75CD)/75D

A = 11D^{2}/75D = 11D/75

47 = C + C^{2} + AC + AB + AD

47 = C + C^{2} + 11CD/75 + 11BC/75 + 11D^{2}/75

47 = (C + C^{2} + 11CD/75 + (61875C - 825C^{2}D -825CD -946CD^{2})/5625D +
11D^{2})/75

3525 = C + C^{2} + 11CD/75 + (61875C - 825C^{2}D -825CD -946CD^{2})/5625D +
11D^{2}

19,828,125^{ = }5625CD + 5625C^{2}D
+ 825CD^{2} + 61875C - 825C^{2}D
-825CD -946CD^{2} + 61875D^{3}

19,828,125^{ = }4800CD + 4800C^{2}D
- 121CD^{2} + 61875C + 61875D^{3}

75 = D + D^{2} + AD + BD + CD

75 = D + D^{2} + 11D^{2}/75
+ (5625 -75CD -75D - 86D^{2})/75 + CD

5625 = 75D + 75D^{2} + 11D^{2}
+ 5625 -75CD -75D - 86D^{2} + 75CD

0 = 0D + 0D^{2 }+ 0D^{ }+ 0CD^{ }

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