Statistics?

Question

a company's HR officer reports a breakdown of employees by job type and gender, shown in the table

Management 7 male 6Female
Supervision 8 male 12 female
production 45 male 72 female
whats the probabilityu that a worker selected at random is
a. female
b. female or a production worker
c. female, if the person works in production
d a production worker, if the person is female.

I tried several times and couldt get the correct answer if someone can help/explain i would appreciate it.thanks

Answer 1

Mgmt: 7M 6F 13tot
Supr: 8M 12F 20tot
Prod: 45M 72F 117tot

tot 60M 90F 150tot
p(F) 90/150 = 3/5 = .60
p(F or Prod) 90/150+ 117/150 - 72/150 (p(Fandprod)) = 135/150 =9/10 = .90
p(F and prod) = 72/117 = .62
p (prod and F) 72/90 = 8/10 = .80