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:

Monthly income (in Rs)	Number of Television/household
	0	1	2	Above 2
< 10000	20	80	10	0
10000 – 14999	10	240	60	0
15000 – 19999	0	380	120	30
20000 – 24999	0	520	370	80
25000 and above	0	1100	760	220

Find the probability:

1. of a household earning Rs 10000 – Rs 14999 per year and having exactly one television.
2. of a household earning Rs 25000 and more per year and owning 2 televisions.
3. 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 ₹ 10000 – ₹ 14999 per yer and having exactly one television, n(E₁) = 240

∴ Required probability = `(n(E_1))/(n(S))`

= `240/4000`

= `6/100`

= `3/50`

= 0.06

Hence, the probability of a household earning ₹ 10000 – ₹ 14999 per year and having exactly one television is 0.06.

ii. Number of households earning ₹ 25000 and more per year owning 2 televisions, n(E₂) = 760

∴ Required probability = `(n(E_2))/(n(S))`

= `760/4000`

= 0.19

Hence, the probability of a household earning ₹ 25000 and more per year owning 2 televisions is 0.19.

iii. Number of households not having any television, n(E₃) = 30

∴ Required probability = `(n(E_3))/(n(S))`

= `30/4000`

= `3/400`

Hence, the probability of a household not having any television is `3/400`.