Question

An insurance company insured 2000 scooter drivers. 4000 car drivers and 6000 truck drivers. The probability of an accidents are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Solution

Let E₁ , E₂, E₃ be the events that the insured person is scooter driver, car driver, truck driver respectively.

therefore space space space straight P left parenthesis straight E subscript 1 right parenthesis space equals space fraction numerator 2000 over denominator 2000 plus 4000 plus 6000 end fraction space equals space 2000 over 12000 space equals space 1 over 6 space space space space space space straight P left parenthesis straight E subscript 2 right parenthesis space equals space fraction numerator 4000 over denominator 2000 plus 4000 plus 6000 end fraction space equals space 4000 over 12000 equals 1 third space space space space space straight P left parenthesis straight E subscript 3 right parenthesis space equals space fraction numerator 6000 over denominator 2000 plus 4000 plus 6000 end fraction equals space 6000 over 12000 equals space 1 half

Let E be the event that an insured person meets with an accident.

straight P left parenthesis straight E divided by straight E subscript 1 right parenthesis space equals space 0.01 comma space space space space straight P left parenthesis straight E divided by straight E subscript 2 right parenthesis space equals space 0.03 comma space space space straight P left parenthesis straight E divided by straight E subscript 3 right parenthesis space equals space 0.15

straight P left parenthesis straight E subscript 1 divided by straight E right parenthesis space equals space fraction numerator straight P left parenthesis straight E subscript 1 right parenthesis thin space straight P left parenthesis straight E divided by straight E subscript 1 right parenthesis over denominator straight P left parenthesis straight E subscript 1 right parenthesis thin space straight P left parenthesis straight E divided by straight E subscript 1 right parenthesis space plus space straight P left parenthesis straight E subscript 2 right parenthesis space straight P left parenthesis straight E divided by straight E subscript 2 right parenthesis space plus space straight P left parenthesis straight E subscript 3 right parenthesis thin space straight P left parenthesis straight E divided by straight E subscript 3 right parenthesis end fraction space space space space space space space space space space space space space space space space space

equals space fraction numerator open parentheses begin display style 1 over 6 end style close parentheses space left parenthesis 0.01 right parenthesis over denominator open parentheses begin display style 1 over 6 end style close parentheses space left parenthesis 0.01 right parenthesis space plus space begin display style 1 third end style left parenthesis 0.03 right parenthesis space plus space begin display style 1 half end style left parenthesis 0.15 right parenthesis end fraction space equals space fraction numerator begin display style 1 over 6 end style cross times begin display style 1 over 100 end style over denominator begin display style 1 over 6 end style cross times begin display style 1 over 100 end style plus begin display style 1 third end style cross times begin display style 3 over 100 end style plus begin display style 1 half end style cross times begin display style 15 over 100 end style end fraction equals space fraction numerator begin display style 1 over 6 end style over denominator begin display style 1 over 6 end style plus begin display style 3 over 3 end style plus begin display style 15 over 2 end style end fraction equals space fraction numerator 1 over denominator 1 plus 6 plus 45 end fraction space equals space 1 over 52

For Daily Free Study Material Join wiredfaculty