An insurance company estimated that 30% of all automobile accidents were caused

Question

An insurance company estimated that 30% of all automobile accidents were caused by weather conditions and 20% of all automobile accidents involved bodily injury. Further, of the accidents that involved bodily injury and were caused by weather conditions were estimated to be 12%

Fill in the table below:

Then answer questions:

a) What is the probability that a randomly chosen accident both was caused by weather conditions and did not involve bodily injury?

b) What is the probability that a randomly chosen accident both was not caused by weather conditions and did notinvolve bodily injury?

c) Are the events "caused by weather conditions" and "involved in bodily injury" independent? Explain?

Explanation / Answer

P(A)=0.3 P(B)=0.2 P(AuB)=0.12

the table filled looks as follows: 12% 18% 30%

8% 62% 70%

20% 80% 100%

a) frm the matrix P(a)=0.18

b) frm the matrix P(b)=0.62

c) No they are not mutually exclusive since both the events can happen at the same time.

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