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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 42
Total: 101
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 ?
Solution:  
Let E1 : ‘Insured person is a scooter driver’, E2 : ‘Insured person is a car driver’ and E3 : ‘Insured person is truck driver’
⇒P(E1)=
2000
2000+4000+6000
=
1
6

⇒P(E2)=
4000
2000+4000+6000
=
1
3

⇒P(E3)=
6000
2000+4000+6000
=
1
2

Let A : ‘Insured person meets with an accident’,
then P(A|E1)=0.01=
1
100
,
P(A|E2)=0.03=
3
100

P(A|E3)=0.15=
15
100

Required probability
=P(E1|A)=
P(A|E1)P(E1)
P(A|E1)P(E1)+P(A|E2)P(E2)+P(A|E3)P(E3)
=
1
100
×
1
6
(
1
100
×
1
6
)+(
3
100
×
1
3
)+(
15
100
×
1
2
)
=
1
52
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