Question

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

$\begin{array}{cccccc}\text{Age(in years)}& 20-29& 30-39& 40-49& 50-59& 60\text{and above}\\ \text{Number of}& 38& 27& 86& 46& 3\\ \text{workers}& & & & & \end{array}$

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.

Answer 1

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

(i) Number of persons selected at the age of 40 years or more,
$n\left(E_1\right)=86+46+3=135$
$\therefore$ Probability that the persons selected at the age of 40 years or more,
$P\left(E_1\right)=\frac{n\left(E_1\right)}{n\left(S\right)}=\frac{135}{200}=0.675$

(ii) Number of persons selected under the age of 40 years,
$n\left(E_2\right)=38+27=65$
$\therefore$ Probability that the persons selected under the age of 40 years,
$P\left(E_1\right)=\frac{n\left(E_2\right)}{n\left(S\right)}=\frac{65}{200}=0.325$

(iii) Number of persons selected having age from 30 to 39 years,
$n\left(E_3\right)=27$
$\therefore$ Probability that the persons selected having age from 30 to 39 years,
$P\left(E_3\right)=\frac{n\left(E_3\right)}{n\left(S\right)}=\frac{27}{200}=0.135$

(iv) Number of persons selected having age under 60 nut over 39 years,
$n\left(E_4\right)=86+46=132$
$\therefore$ Probability that the persons selected having age under 60 but over 39 years,
$P\left(E_4\right)=\frac{n\left(E_4\right)}{n\left(S\right)}=\frac{132}{200}=0.66$