**Question:**

A company selected 2400 families at random and surveys them to determine a relationship between income level and the number of vehicles in a home. The information gathered is listed below:

Vechicles Per Family:

If a family is chosen at random find the probability that the family is:

1. Earning Rs 10000 – 13000 per month and owning exactly 2 vehicles.

2. Earning Rs 16000 or more per month and owning exactly 1 vehicle.

3. Earning less than Rs 7000 per month and does not own any vehicle.

4. Earning Rs 13000 – 16000 per month and owning more than 2 vehicles.

5. Owning not more than 1 vehicle.

6. Owning at least one vehicle

**Solution:**

1. The probability that the family is earning 10000-13000 and is having exactly 2 vehicles

$=\frac{\text { No of families having } 10000-13000 \text { income and } 2 \text { vehicles }}{\text { Total no of families }}$

= 29/2400

2. The probability that the family is earning 16000 or more and is having exactly 1 vehicle

$=\frac{\text { No of families having } 16000 \text { or more income and } 1 \text { vehicle }}{\text { Total no of families }}$

= 579/2400

3. The probability that the family is earning less than 7000 and is having no vehicle

$=\frac{\text { No of families having less than } 7000 \text { income and no vehicle }}{\text { Total no of families }}$

= 25/2400 = 196

5. The probability that the family is having not more than one vehicle

$=\frac{\text { No of families having not more than } 1 \text { vehicle }}{\text { Total no of families }}$

$=\frac{10+0+1+2+1+160+305+535+469+579}{1200}$

= 2062/2400

= 1031/1200

6. The probability that the family is having at least one vehicle

$=\frac{\text { No of families having at least } 1 \text { vehicle }}{\text { Total no of families }}$

$=\frac{160+305+535+469+579+25+27+29+29+82+0+2+1+25+88}{1200}$

= 2356/2400

= 589/600