Question

Question 16
A company selected 4000 households at random and surveyed them to find out a relationship between income level and the number of television sets in a home. The information, so obtained is listed in the following table.

Find the probability:
(i) Of a household earning Rs.10000 - Rs.14999 per year and having exactly one television.

(ii) Of a household earning Rs.25000 and more per year owning 2 televisions.

(iii) Of a household not having any television.

Answer 1

The total number of the households selected by the company,
n(S) = 4000

(i) Number of households earning Rs.10000 - Rs. 14999 per year and having exactly one television, $n\left(E_1\right)=240$.
$\therefore$ Required probability $=\frac{n\left(E_1\right)}{n\left(S\right)}=\frac{240}{4000}=\frac{6}{100}=\frac{3}{50}=0.06$
Hence, the probability of a household earning Rs. 10000 - Rs. 14999 per year and having exactly one television is 0.06.

(ii) Number of households earning Rs. 25000 and more per year owning 2 televisions, $n\left(E_2\right)=760$.
$\therefore$ Required probability $=\frac{n\left(E_2\right)}{n\left(S\right)}=\frac{760}{4000}$
$=0.19$
Hence, the probability of a household earning Rs. 25000 and more per year owning 2 televisions is 0.19.

(iii) Number of household not having any television, $n\left(E_3\right)=30$
$\therefore$ Required probability $=\frac{n\left(E_3\right)}{n\left(S\right)}=\frac{30}{4000}=\frac{3}{400}$

Hence, the probability of a household not having any television is $\frac{3}{400}$.