Samples of emissions from three suppliers are classified for conformance to air-quality specifications. the results from 100 samples are summarized as follows:
conforms
yes no
supplier
1 22 8
2 25 5
3 30 10
let a denote the event that a sample is from supplier 1, and let b denote the event that a sample conforms to specifications.
(a) find p(a)
(b) find p(b)
(c) find p(b∣a)
(d) find p(a∪b)
(e) are a and 8 independent? justify your answer.