A company selected 2400 families at random and survey them to determin

1.	A company selected 2400 families at random and survey them to determine a relationship between income level and the number of vehicles in a home. The information gathered is listed in the table below :Monthly income (in Rs.)Vehicles per family012Above 2Less than 7000101602507000-10000030527210000-13000153529113000-160002469292516000 or more15798288If a family is chosen find the probability that the family is:(i) Earning Rs. 10,000 – 13,000 per month and owning exactly 2 vehicles.(ii) Earning Rs. 16,000 or more per month and owning exactly 1 vehicles.(iii) Earning less than Rs. 7,000 per month and does not own any vehicles.(iv) Earning Rs. 13,000 – 16,000 per month and owning more than 2 vehicles.(v) Owning not more than 1 vehicle.(vi) Owning at least one vehicle.
Answer» Given, (i) The probability that the family is earning Rs. 10,000 – 13,000 per month and owning exactly 2 vehicles \(=\frac{favourable \,outcome}{total\,outcome}=\frac{29}{2400}\) (ii) The probability that the family earning Rs. 16,000 or more per month and owning exactly 1 vehicles \(=\frac{favourable \,outcome}{total\,outcome}=\frac{579}{2400}\) (iii) The probability that the family earning less than Rs. 7,000 per month and does not own any vehicles \(=\frac{favourable \,outcome}{total\,outcome}=\frac{10}{2400}=\frac{1}{240}\) (iv) The probability that the family earning Rs. 13,000 – 16,000 per month and owning more than 2 vehicles \(=\frac{favourable \,outcome}{total\,outcome}=\frac{25}{2400}=\frac{1}{96}\) (v) The probability that the family owning not more than 1 vehicle \(=\frac{favourable \,outcome}{total\,outcome}=\frac{10+0+1+2+1+160+305+535+469+579}{2400}\) \(=\frac{2062}{2400}=\frac{1031}{1200}\) (vi) The probability that the family owning at least one vehicle \(=\frac{favourable \,outcome}{total\,outcome}\) \(=\frac{160+305+535+469+579+254+27+29+29+82+0+2+1+25+86}{2400}\) \(=\frac{2356}{2400}=\frac{589}{600}\)

A company selected 2400 families at random and survey them to determine a relationship between income level and the number of vehicles in a home. The information gathered is listed in the table below :Monthly income (in Rs.)Vehicles per family012Above 2Less than 7000101602507000-10000030527210000-13000153529113000-160002469292516000 or more15798288If a family is chosen find the probability that the family is:(i) Earning Rs. 10,000 – 13,000 per month and owning exactly 2 vehicles.(ii) Earning Rs. 16,000 or more per month and owning exactly 1 vehicles.(iii) Earning less than Rs. 7,000 per month and does not own any vehicles.(iv) Earning Rs. 13,000 – 16,000 per month and owning more than 2 vehicles.(v) Owning not more than 1 vehicle.(vi) Owning at least one vehicle.

Answer»

Given,

(i) The probability that the family is earning Rs. 10,000 – 13,000 per month and owning exactly 2 vehicles \(=\frac{favourable \,outcome}{total\,outcome}=\frac{29}{2400}\)

(ii) The probability that the family earning Rs. 16,000 or more per month and owning exactly 1 vehicles \(=\frac{favourable \,outcome}{total\,outcome}=\frac{579}{2400}\)

(iii) The probability that the family earning less than Rs. 7,000 per month and does not own any vehicles \(=\frac{favourable \,outcome}{total\,outcome}=\frac{10}{2400}=\frac{1}{240}\)

(iv) The probability that the family earning Rs. 13,000 – 16,000 per month and owning more than 2 vehicles \(=\frac{favourable \,outcome}{total\,outcome}=\frac{25}{2400}=\frac{1}{96}\)

(v) The probability that the family owning not more than 1 vehicle \(=\frac{favourable \,outcome}{total\,outcome}=\frac{10+0+1+2+1+160+305+535+469+579}{2400}\)

\(=\frac{2062}{2400}=\frac{1031}{1200}\)

(vi) The probability that the family owning at least one vehicle \(=\frac{favourable \,outcome}{total\,outcome}\)

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