1) An insurancecompany estimated that 30% of all automobile accidents werepartly

Question

1) An insurancecompany estimated that 30% of all automobile accidents werepartly

caused by weatherconditions and the 20% of all automobile accidentsinvolved

bodily injury.Further, of those accidents that involved bodily injury, 40%were

partly caused byweather conditions.

a) What is theprobability that a randomly chosen accident both was partly causedby

weather conditions andinvolved bodily injury?

b) Are the events“partly caused by weather conditions” and“involved bodily injury”

independent?

c) If a randomlychosen accident was partly caused by weather conditions, whatis

the probability thatit involved bodily injury?

d) What is theprobability that a randomly chosen accident both was notpartly

caused by weather conditions anddid not involve bodily injury?

Explanation / Answer

Given P(W)=.3, P(I)=.2 and P(W/I)=.4 a)P(WnI)=P(W/I)P(I)=.4(.2)=.08 b)Are W and I independent? To be independent P(WnI)=P(W)+P(I). They are not equal, so they areNOT independent. c)P(I/W)=P(WnI)/P(W)=.08/.3=.27 d)The event W'nI' is by De Morgan's law = Not (WuI). Now P(WuI)=P(W)+P(I)-P(WnI)=.3+.2-.08=.42 Hence, P[not(WuI)]=.58

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