Help with Economics Statistics question Please

I have been staring at the question for at least an hour now and have know idea how to do it, the answer is 0.444 but don't know how to get there, please help if you can!

An economic consultancy has examined the prot growth levels of a large sample of companies in the UK. 25% of all companies reported a prot growth level much better than the national average. 50% reported a prot growth level about the same as the national average, and the remaining 25% reported a prot growth level much worse than the national average. Of those companies which performed much better than the national average, 40% were in the manufacturing sector. Of those companies which performed about the same as the national average, 20% were in the manufacturing sector, as were 10% of those companies which performed much worse than the national average. What is the probability that a randomly selected company in the manufacturing sector had performed much better than the national average?

Thanks :)

Since you have percents, think of 100 companies surveyed. (So 25 companies were above average, 50 same, 25 below).

How many companies are in the manufacturing sector?
40% of 25 companies = 10
20% of 50 companies = 10
10% of 25 companies = 2.5

Therefore, a total of 22.5 companies are in the manufacturinf sector.

For the probability of the company doing better:
There are 10 companies (man sect) which did better.
So the Probability is 10 / 22.5 = 0.4444

I hope this helps you.

Note: When you have percents to work with, it is okay to pretend you have a set number (100 is easy), Then you can see the totals more readily. The proportions will be the same.

BAYES theorem of probability is used
Required probability = (0.25*0.4) / ((0.25*0.4)+(0.50*0.2)+(0.25*0.1))
= 0.100 / (0.100+0.100+0.025)
= 0.100 / 0.225
= 4/9 OR 0.444444444