Question

An organisation selected 2400 families at random and surveyed them to determine relationship between income level and the number of vechicles in a family. The information gathered is listed in the table below:

Suppose a family is chosen. Find the probability that the family chosen is :
(i) earning Rs. 10000-13000 per month and owning exactly 2 vehicles.
(ii) earning Rs. 16000 or more per month and owning exactly 1 vehicle.
(iii) earning less than Rs. 7000 per month and does not own any vehicle.
(iv) earning Rs. 13000-16000 per month and owning more than 2 vehicles.
(v) owning not more than 1 vehicle.

Answer 1

Total number of families selected by the organisation, n(S) = 2400
(i) The number of families earning Rs. 10000-13000 per month and owing exactly 2 vehicles,
`n(E_(1))=29`
`therefore" Required probability"=(n(E_(1)))/(n(S))=(29)/(24000)`
(ii) The number of families earning Rs. 16000 or more per month and owing exactly 1 vehicle,
`n(E_(2))=579`
`therefore" Required probability"=(n(E_(2)))/(n(S))=(579)/(2400)`
(iii)The number of families earning less than Rs. 7000 per month and does not own any vehicle,
`n(E_(3))=10`
`therefore" Required probaility" = (n(E_(3)))/(n(S))=(10)/(2400)=(1)/(240)`
(iv) The number of families earning Rs. 13000-16000 per month and owing more than 2 vehicles,
`n(E_(4))=25`
`therefore" Required probability" = (n(E_(4)))/(n(S))=(25)/(2400)=(25)/(2400)=(1)/(96)`
(v) The number of families owing not more than 1 vechicle,
`n(E_(5))=(10+1+2+1)+(160+305+535+469+579)=2062`
`therefore" Required probability"=(n(E_(5)))/(n(S))=(2062)/(2400)=(1031)/(1200)`