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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:
- of a household earning Rs 10000 – Rs 14999 per year and having exactly one television.
- of a household earning Rs 25000 and more per year and owning 2 televisions.
- of a household not having any television.
Solution
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`.
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