Question 2 0 A recent survey found that ages of workers in a factory as follows-Whline Agein years - 20-29 - 30 - 39 - 40-49 - 50-59 - 60 and above IWhline Number - of - 38 - 27 - 86 - 46 - 3 workers - - - - - Whline array If a person is selected at random- find the probability that the person is-i 40 years or more-ii Under 40 years-iii Having age from 30 - 39 years-iv Under 60 but over 39 years-

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Experimental/Empirical Probability

Question 2 0 ...

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Question 20
A recent survey found that ages of workers in a factory as follows:

$\begin{matrix} A g e (i n y e a r s) & 20 - 29 & 30 - 39 & 40 - 49 & 50 - 59 & 60 a n d a b o v e N u m b e r o f & 38 & 27 & 86 & 46 & 3 w o r k e r s \end{matrix}$

If a person is selected at random, find the probability that the person is:
(i) 40 years or more.
(ii) Under 40 years.
(iii) Having age from 30 - 39 years.
(iv) Under 60 but over 39 years.

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Solution

Total number of workers in the factory,
$n (S) = 38 + 27 + 86 + 46 + 3 = 200$

(i) Number of persons selected at the age of 40 years or more,
$n (E_{1}) = 86 + 46 + 3 = 135$
$∴$ Probability that the persons selected at the age of 40 years or more,
$P (E_{1}) = \frac{n (E_{1})}{n (S)} = \frac{135}{200} = 0.675$

(ii) Number of persons selected under the age of 40 years,
$n (E_{2}) = 38 + 27 = 65$
$∴$ Probability that the persons selected under the age of 40 years,
$P (E_{1}) = \frac{n (E_{2})}{n (S)} = \frac{65}{200} = 0.325$

(iii) Number of persons selected having age from 30 to 39 years,
$n (E_{3}) = 27$
$∴$ Probability that the persons selected having age from 30 to 39 years,
$P (E_{3}) = \frac{n (E_{3})}{n (S)} = \frac{27}{200} = 0.135$

(iv) Number of persons selected having age under 60 nut over 39 years,
$n (E_{4}) = 86 + 46 = 132$
$∴$ Probability that the persons selected having age under 60 but over 39 years,
$P (E_{4}) = \frac{n (E_{4})}{n (S)} = \frac{132}{200} = 0.66$

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