An independent research team inspects 300 batteries manufactured by two companies for being good or defective. The following table gives the two-way classification of these 300 batteries.
Good
Defective
Company A
140
10
Company B
130
20
a. The team selects one battery randomly from these 300 batteries. Find the probability that this battery:
(i) is manufactured by company B
(ii) is defective
(iii) is good given that it is manufactured by company B
(iv) is manufactured by company A given that it is defective
b. Are the events "company A" and "defective" mutually exclusive? Explain why or why not.
c. Are the events "good" and "company A" independent? Explain why or why not.
d. What is the complimentary event of the event "defective'? What is the probability of this complimentary event?