Small cars get better gas mileage, but are not as safe as bigger cars. Small cars accounted for 18% of vehicles on the road, but accidents involving small cars led to 11,898 fatalities during a recent year. Assume the probability a small car is involved in an accident is .18. The probability of an accident a involving a small car leading to a fatality is .128 and the probability of an accident not involving a small car leading to a fatality is .05. Suppose you learn of an accident involving a fatality. What is the probability a small car was involved? Assume that the likelihood of getting into an accident is independent of car size.
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