Question

An organisation selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below: Monthly income (in ₹)Vehicles per family012Above 2Less than 7000101602507000-10000030527210000-13000153529113000-160002469592516000 or more15798288 Suppose a family is chosen. Find the probability that the family chosen is (i) earning ₹10000 – 13000 per month and owning exactly 2 vehicles. (ii) earning ₹16000 or more per month and owning exactly 1 vehicle. (iii) earning less than ₹7000 per month and does not own any vehicle. (iv) earning ₹13000 – 16000 per month and owning more than​

Answer 1

Step-by-step explanation:

Given

According to the given data

Total number of families = 2400

(i) earning ₹10000 – 13000 per month and owning exactly 2 vehicles.

The probability that the family chosen is earning ₹10000 – 13000 per month and owning exactly 2 vehicles =

(Numbers of families earning ₹10000 –13000 per month and owning exactly 2 vehicles) / (Total number of families)

= 29/2400

(ii) earning ₹16000 or more per month and owning exactly 1 vehicle.

Number of families earning ₹16000 or more per month and owning exactly 1 vehicle = 579

The probability that the family chosen is earning ₹16000 or more per month and owning exactly 1 vehicle =

(Number of families earning ₹16000 or more per month and owning exactly 1 vehicle) / (Total number of families)

=579/2400

(iii) earning less than ₹7000 per month and does not own any vehicle.

Number of families earning less than ₹7000 per month and does not own any vehicle = 10

The probability that the family chosen is earning less than ₹7000 per month and does not own any vehicle =

(Number of families earning less than ₹7000 per month and does not own any vehicle)/(Total number of families)

= 10/2400 = 1/240

(iv) earning ₹13000 – 16000 per month and owning more than 2 vehicles.

Number of families earning ₹13000-16000 per month and owning more than 2 vehicles = 25

The probability that the family chosen is earning ₹13000 – 16000 per month and owning more than 2 vehicles =

(Number of families earning ₹13000-16000 per month and owning more than 2 vehicles ) / (Total number of families)

= 25/2400 = 1/96

(v) owning not more than 1 vehicle.

Number of families owning not more than 1 vehicle = 10+160+0+305+1+535+2+469+1+579 = 2062

The probability that the family chosen owns not more than 1 vehicle = 2062/2400 = 1031/1200

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