According to the Welders Association of America, during the decade from 1980-1989, 40% of injuries incurred by its members were to the eye; 22% were to the hand; 20% to the back; and the remaining 18% of injuries were categorized as "others." Stating whatever assumptions are necessary,
(i) Determine the probability of recording 4 eye injuries, 3 hand injuries, 2 hand injuries, and 1 injury of the "other" variety.
(ii) Of 5 total recorded injuries, what is the probability that fewer than 2 are eye injuries?
(iii) Because eye injuries are the most prevalent, and the most costly to treat, it is desired to reduce their occurrences by investing in eye-safety training programs for the association's members. What target probability of a single occurrence of an eye injury should the program aim for in order to achieve an overall objective of increas- ing to approximately 0.9 the probability of observing fewer than 2 eye injuries?