Smallest Safest Car
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Chicco DJ Baby Walker, Splash $69.99 … |
MATH – What is the probability a small car was involved in the accident (to 2 decimals)?
Small cars get better gas mileage, but they are not as safe as bigger cars. Small cars accounted for 18% of the vehicles on the road, but accidents involving small cars led to 11,898 fatalities during a recent year (Reader’s Digest, May 2000). Assume the probability a small car is involved in an accident is .18. The probability of a fatality in an accident involving a small car is .128 and the probability of a fatality in an accident involving a bigger car is .05. Suppose you learn about an accident involving a fatality.
What is the probability a small car was involved in the accident (to 2 decimals)?
p(fatal | small) = 0.128
p(fatal | large) = 0.05
p(small) = 0.18
=> p(large) = 0.82
p(small AND fatal) = p(small) * p(fatal | small) = 0.18 * 0.128 = 0.02304
p(large AND fatal) = p(large) * p(fatal | large) = 0.82 * 0.05 = 0.041
p(fatal) = p(small AND fatal) + p(large AND fatal) = 0.02304 + 0.041 = 0.06404
p(small AND fatal) = p(fatal) * p(small | fatal)
=> p(small | fatal) = p(small AND fatal) / p(fatal) = 0.02304 / 0.06404 = 0.36
Smallest Safest Car
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