Question

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,
$n\left(S\right)=4000$

(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 $\mathrm{0.06.}$

(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 $\mathrm{0.19.}$

(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 $\frac{3}{400}$.