Question

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

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

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 $Rs.210$.

Answer 1

Number of total workers $\left(n\right)=30$

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

A worker is selected

(i) No. of workers having less than $Rs.150\left(m\right)=3+4=7$

$\therefore$ Probability P(A) =$\frac{m}{n}=\frac{7}{30}$

(ii) No. of workers having at least $Rs.210\left(m\right)=4+3=7$

$\therefore$ Probability P(A) =$\frac{m}{n}=\frac{7}{30}$

(iii) No. of workers having more than or equal to $Rs.150$ but less than $Rs.210$ $=5+6+5=16$

$\therefore$ Probability P(A) =$\frac{m}{n}=\frac{16}{30}=\frac{8}{15}$