Question

A survey of local companies reveals that 65% of all local companies plan to increase employment over the next 6 months. Furthermore, 75% of all local companies currently have fewer than 100 employees. Finally, 80% of those with less than 100 employees said they planned on increasing employment over the next 6 months. Of the companies with more than 100 employees, what is the probability a company selected at random, plans on increasing employment over the next 6 months? (please round your answer to 2 decimal places)

Answer 1

Let X is the total number of companies.
Among them, 0.65*x number of companies plan to increase employment.
0.75*x number of companies have less than 100 employees.
0.75*0.8*x=0.6x companies among the company having less than 100 employees planned on increasing employment over the next 6 months.
The number of companies left who has planned to increase employement=0.65x-0.6x=0.05x.
The number of companies having more than 100 employees =0.25x

Of the companies with more than 100 employees, what is the probability a company selected at random, plans on increasing employment over the next 6 months=0.05x/0.25x=0.2