Given below is the frequency distribution of wages in Rs of 30 workers in a certain factory- Wages in Rs 110-130 130-150 150-170 170-190 190-210 210-230 230-250 -No- of workers 3 5- 6 5 4 3 -A worker is selected at random- Find the probability that his wages are-i less than Rs 150ii at least Rs 210iii more than or equal to 150 but less than Rs 210 -

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Standard IX

Mathematics

Trail

Given below i...

Question

Given below is the frequency distribution of wages (in Rs) of 30 workers in a certain factory:

Wages (in Rs) 110-130 130-150 150-170 170-190 190-210 210-230 230-250

No. of workers 3 4 5 6 5 4 3

A worker is selected at random. Find the probability that his wages are:
(i) less than Rs 150
(ii) at least Rs 210
(iii) more than or equal to 150 but less than Rs 210.

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Solution

The total number of trials is 30.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

(i) Let A₁ be the event that the wages of a worker is less than Rs 150.

The number of times A₁ happens is.

Therefore, we have.

(ii) Let A₂ be the event that the wages of a worker is atleast Rs 210.

The number of times A₂ happens is.

Therefore, we have.

(iii) Let A₃ be the event that the wages of a worker is more than or equal to Rs 150 but less than Rs 210.

The number of times A₃ happens is.

Therefore, we have

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Similar questions

Given below is frequency distrigution of wages (in Rs ) of 30 workers in certain factory:

$\begin{matrix} Wages (in Rs) & 110 - 130 & 130 - 150 & 150 - 170 & 170 - 190 & 190 - 210 & 210 - 230 & 230 - 250 No.of workers & 3 & 4 & 5 & 6 & 5 & 4 & 3 \end{matrix}$

A worker is selected at random. Find the probability that his wages are:

(i) less than $R s . 150$ (ii) at least $R s . 210$ (iii) more than or equal to $150$ but less than $R s . 210$ .

Q. Express the number of workers with wages less than Rs 110 as the percent of the number of workers with wages more than Rs 100.

Q. The following table given the weekly wages (in Rs.) of workers in a factory:

Weekly wages (in Rs.)	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$	$80 - 85$	$85 - 90$
No. of workers	$5$	$20$	$10$	$10$	$9$	$6$	$12$	$8$

Calculate: the number of workers getting

R s . 65

or more but less than

R s . 85

as weekly wages.

Q. The weekly wages (in Rs.) of 30 workers in a factory are given:
830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840
Mark a frequency table with intervals as 800-810, 810-820 and so on, using tally marks. Also, draw a histogram and answer the following questions:
(i) Which group has the maximum number of workers?
(ii) How many workers earn Rs 850 and more?
(iii) How many workers earn less than Rs 850?

Q. An average daily wages of

10

workers in a factory '

A

' is Rs.

30

and an average daily wages of

20

workers in a factory '

B

' is Rs.

15

. Find the average daily wages of all workers of both the factories.

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Wages (in Rs)	110-130	130-150	150-170	170-190	190-210	210-230	230-250
No. of workers	3	4	5	6	5	4	3