Given below is the frequency distribution of wages (in ₹ ) of $30$ workers in a certain factory:
Wages $(i n ₹)$ Number of workers
$210 - 230$ $4$
$230 - 250$ $3$
$250 - 270$ $6$
$270 - 290$ $5$
$290 - 310$ $4$
$310 - 330$ $5$
$330 - 350$ $3$
A worker is selected at random. Find the probability that his wages are: (i) less than ₹ $250$ (ii) at least ₹ $310$ (iii) more than or equal to ₹ $250$ but less than ₹ $310$

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Solution

Given,
Total number of workers $= 30$
Number of workers who have wages less than ₹ $250$ $= 4 + 3 = 7$
Number of workers who have wages of at least ₹ $310$ $= 5 + 3 = 8$
Number of workers who have wages more than or equal to ₹ $250$ but less than ₹ $310$ $= 6 + 5 + 4 = 15$
We use the formula,
Probability of favorable outcome $P = \frac{N u m b e r o f f a v o r a b l e o u t c o m e s}{T o t a l n u m b e r o f w o r k e r s}$
Find the probability that his wages
(i) less than ₹ $250$ $P = \frac{N u m b e r o f w o r k e r s w h o h a v e w a g e s l e s s t h a n ₹ 250}{T o t a l n u m b e r o f w o r k e r s} = \frac{7}{30}$
(ii) at least ₹ $310$ $P = \frac{N u m b e r o f w o r k e r s w h o h a v e w a g e s o f a t l e a s t ₹ 310}{T o t a l n u m b e r o f w o r k e r s} = \frac{8}{30} = \frac{4}{15}$
(iii) more than or equal to ₹ $250$ but less than ₹ $310$ $P = \frac{N u m b e r o f w o r k e r s w h o h a v e w a g e s m o r e t h a n o r e q u a l t o ₹ 250 b u t l e s s t h a n ₹ 310}{T o t a l n u m b e r o f w o r k e r s} = \frac{15}{30} = \frac{1}{2}$
Hence, the probability of workers' wages are
(i) less than ₹ $250$ is $\frac{7}{30}$
(ii) at least ₹ $310$ is $\frac{4}{15}$
(iii) more than or equal to ₹ $250$ but less than ₹ $310$ is $\frac{1}{2}$ .

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Similar questions

Q. 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.

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. A grouped frequency table with class intervals of equal sizes using

250 - 270

(

270

not included in this interval) as one of the class interval is constructed for the following data :

268, 220, 368, 258, 242, 310, 272, 342,

310, 290, 300, 320, 319, 304, 402, 318,

406, 292, 354, 278, 210, 240, 330, 316,

406, 215, 258, 236.

The frequency of the class

310 - 330

is:

Question 8
A grouped frequency table with class intervals of equal sizes using 250 – 270 (270 not included in this interval) as one of the class intervals is constructed for the following data.

268, 220, 368, 258, 242, 310, 272, 342

310, 290, 300, 320, 319, 304, 402, 318

406, 292, 354, 278, 210, 240, 330, 316,
406, 215, 258, 236.

The frequency of class 310 - 330 is:

A) 4
B) 5
C) 6
D) 7

Q. Following figures relate the weekly wages (in Rs.) of 15 workers in a factory:
300, 250, 200, 250, 200, 150, 350, 200, 250, 200, 150, 300, 150, 200, 250

Prepare a frequency table,

(i) What is the range in wages (in Rs)?
(ii) How many Workers are getting Rs 350?
(iii) How many workers are getting the minimum wages?

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Wages $(i n ₹)$	Number of workers
$210 - 230$	$4$
$230 - 250$	$3$
$250 - 270$	$6$
$270 - 290$	$5$
$290 - 310$	$4$
$310 - 330$	$5$
$330 - 350$	$3$