Question

Find
Ques) A recent survey found that the ages of workers in a factory are distributed as follows:-

Age (in yrs)	No. of workers
20-29	38
30-39	27
40-49	86
50-59	46
60 $ above	3

If a person is selected at random, find the probability that the person is:
a) 40 years or more
b) Under 40 years
c) Having age from 30 to 39 years.

Answer 1

Dear Student,
Here is the solution of your asked query:
$$\begin{gathered} \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{workers}=38+27+86+46+3=200 \\ \mathrm{a})\mathrm{Total}\mathrm{person}\mathrm{more}\mathrm{than}40\mathrm{years}=86+46+3=135 \\ \mathrm{so},\mathrm{probability}\mathrm{of}\mathrm{getting}\mathrm{person}\mathrm{more}\mathrm{than}40\mathrm{years}=\frac{\mathrm{Total}\mathrm{person}\mathrm{more}\mathrm{than}40\mathrm{years}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{workers}} \\ =\frac{135}{200} \\ =\frac{27}{40} \\ \mathrm{b})\mathrm{Total}\mathrm{person}\mathrm{under}40\mathrm{years}=38+27=65 \\ \mathrm{So},\mathrm{probability}\mathrm{of}\mathrm{getting}\mathrm{person}\mathrm{more}\mathrm{under}40\mathrm{years}=\frac{\mathrm{Total}\mathrm{person}\mathrm{under}40\mathrm{years}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{workers}} \\ =\frac{65}{200} \\ =\frac{13}{40} \\ \mathrm{c})\mathrm{Total}\mathrm{person}\mathrm{under}\mathrm{having}\mathrm{age}\mathrm{from}30\mathrm{to}39\mathrm{years}=27 \\ \mathrm{So},\mathrm{probability}\mathrm{of}\mathrm{getting}\mathrm{person}\mathrm{having}\mathrm{age}\mathrm{from}30\mathrm{to}39\mathrm{years}=\frac{\mathrm{Total}\mathrm{personhaving}\mathrm{age}\mathrm{from}30\mathrm{to}39\mathrm{years}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{workers}} \\ =\frac{27}{200} \end{gathered}$$
Regards