Two questions I need some help with,

First question. This has something to do with expectations and its properties.

The sales per day for a product is estimated as follows based on past records

Daily demand (X) / Probaility

10 / .1

11 / .2

12 / .4

13 / .3

a. Obtain the mean and variance of the daily sales.

b. If the porfit can be described by the equation, profit= -10+(4*X)

What is the expected daily profit? What is the variance of the daily profit?

2. An insurance company runs three offices, A, B and C. The company's employess are distirbuted as follows; 30% work in office A, 20% in Off. B and 505 in Off. C.

In office A 10% are managers, in office B 20% are managers and in office C 5% are managers

a. What is the total proportion of managers in the company?

b. If a member of staff, randomly chosen, turns out to be a manager, what is the probability that she works in office A.

My answer for part a is 0.095 or 9.5%. I' not sure on part b though, I think it has something to do with conditional probability.